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Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Flogseq____",48,536870918]],[logseq____"^15logseq____",[34,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[34,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[34,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[34,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u6524c646-99c2-4b26-8539-57c4101ad49elogseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&=a^2+2ab+b^2logseq____&,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&=a^2-2ab+b^2logseq____&,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&=a^2-b^2logseq____&,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Flogseq____",47,536870918]],[logseq____"^15logseq____",[35,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u6524c646-387a-4236-806b-1d940c14df8flogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Flogseq____",33,536870918]],[logseq____"^15logseq____",[36,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[36,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[36,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[36,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u6524c646-01a6-44d5-9c2b-02ca554a7785logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Flogseq____",39,536870918]],[logseq____"^15logseq____",[37,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[37,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[37,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[37,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[37,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",2],536870918]],[logseq____"^15logseq____",[37,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[37,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[37,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~u6524c646-eca1-4b93-b222-46ad1316814clogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Flogseq____",67,536870918]],[logseq____"^15logseq____",[38,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[38,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[38,logseq____"^Hlogseq____",26,536870918]],[logseq____"^15logseq____",[38,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u6524c646-b7b5-4848-aad5-141eeef109b9logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Flogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u6524c646-2479-4145-8e63-82bbdddeacdelogseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Flogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[40,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[40,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[40,logseq____"^17logseq____",false,536870918]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u6524c646-2fe5-4695-94fd-3cae2ee5ea38logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Qlogseq____",logseq____"logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Flogseq____",59,536870918]],[logseq____"^15logseq____",[41,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[41,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[41,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u6524c646-a43b-4d5a-93e8-3a3cbae220f9logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Qlogseq____",logseq____"$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Flogseq____",45,536870918]],[logseq____"^15logseq____",[42,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[42,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[42,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u6524c646-0911-497e-8779-4fa6d137af68logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Flogseq____",51,536870918]],[logseq____"^15logseq____",[43,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[43,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[43,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[43,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[43,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[43,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[43,logseq____"^;logseq____",logseq____"~u6524c646-ff70-44b7-8b72-2e0631dab280logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Flogseq____",34,536870918]],[logseq____"^15logseq____",[44,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[44,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[44,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[44,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[44,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u6524c646-7c32-4378-aeae-6030a4b2ed19logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Flogseq____",49,536870918]],[logseq____"^15logseq____",[45,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[45,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[45,logseq____"^Hlogseq____",28,536870918]],[logseq____"^15logseq____",[45,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u6524c646-9c76-48b1-aa42-0a63a5742581logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&=\\\\lg y logseq____& ,r\\\\\\\\\\nxlogseq____&=\\\\log_y10logseq____&,f\\\\\\\\\\nxlogseq____&=\\\\log_{10}ylogseq____&,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 2 logseq____&, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, r \\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Flogseq____",63,536870918]],[logseq____"^15logseq____",[46,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[46,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[46,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u6524c646-f19f-4a08-92d8-71a81cf145f3logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Flogseq____",58,536870918]],[logseq____"^15logseq____",[47,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[47,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[47,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[47,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[47,logseq____"^Hlogseq____",27,536870918]],[logseq____"^15logseq____",[47,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u6524c646-efea-476c-82c6-ed011e13d7a4logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",54,536870918]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[48,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u6524c646-fdac-4a3f-9dc4-dc8f5641d02elogseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Qlogseq____",logseq____"$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",44,536870918]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[49,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u6524c646-190b-4414-bc8c-c1e04e547c05logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&=a^2-b^2\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",64,536870918]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[50,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u6524c646-24f6-43b3-add2-beabe7c5159clogseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",66,536870918]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u6524c646-f7a8-44a9-bef5-c37a505a49e6logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",65,536870918]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[52,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u6524c646-2675-422a-aec2-8d270e980543logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c} (a+b)^0logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 \\\\\\\\\\n(a+b)^1logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^2logseq____&logseq____&logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 2 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^3logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 3 logseq____&logseq____& 3 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^4logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 4 logseq____&logseq____& 6 logseq____&logseq____& 4 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^5logseq____&logseq____&logseq____& 1 logseq____&logseq____& 5 logseq____&logseq____& 10 logseq____&logseq____& 10 logseq____&logseq____& 5 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^6logseq____&logseq____& 1 logseq____&logseq____& 6 logseq____&logseq____& 15 logseq____&logseq____& 20 logseq____&logseq____& 15 logseq____&logseq____& 6 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^7logseq____&1 logseq____&logseq____& 7 logseq____&logseq____&21 logseq____&logseq____& 35 logseq____&logseq____& 35 logseq____&logseq____& \\\\cdots\\\\end{array}logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",37,536870918]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u6524c646-baec-4c0a-99c8-aa4415dfe65alogseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",56,536870918]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[54,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[54,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u6524c646-1922-4c05-87c9-60349b36ee2blogseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(2x+y)^4logseq____&=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5logseq____&=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",53,536870918]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u6524c646-e6d9-499c-b1c7-b9f2397d20e5logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&= \\\\frac1{\\\\ln a}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",46,536870918]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u6524c646-57a8-41e9-9a1c-132654ddeec7logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",62,536870918]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[57,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u6524c646-bf9e-4bf1-aea1-525de52c954alogseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",60,536870918]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u6524c646-0e66-4862-ad20-18ec02f607balogseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",40,536870918]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u6524c646-9e9a-47ed-8361-c335cf129663logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",42,536870918]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u6524c646-1248-4db0-8bff-6db84ddbed5dlogseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&=a^\\\\frac mn\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",52,536870918]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u6524c646-23f0-4342-a9a5-fa26278ea87elogseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{y^2}\\\\notag\\\\\\\\\\nlogseq____&=\\\\left|y\\\\right|\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",61,536870918]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u6524c646-f25c-4aa3-a4ea-9903bd7dde6blogseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",41,536870918]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[63,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[63,logseq____"^Hlogseq____",25,536870918]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u6524c646-ff97-407a-8069-68123348de80logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\na^nlogseq____&=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____& a,blogseq____>0\\\\\\\\\\na^2b^2logseq____&=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&=a^{nm}\\\\\\\\\\na^0logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",43,536870918]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u6524c646-af24-43a3-8a31-63e836d87245logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",36,536870918]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[65,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u6524c646-269d-41ce-96a4-cffa13d03ab0logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",38,536870918]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[66,logseq____"^Hlogseq____",30,536870918]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u6524c646-6d3e-4599-baff-7e3a3483ff74logseq____",536870918]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist 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