erweitern (5x^6+2x^3)^4

Lösung

erweitern

(5 x^{6} + 2 x^{3})^{4}

625 x^{24} + 1000 x^{21} + 600 x^{18} + 160 x^{15} + 16 x^{12}

Schritte zur Lösung

(5 x^{6} + 2 x^{3})^{4}

Wende Binomialsetz an:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 5 x^{6}, b = 2 x^{3}

= i = 0 \sum 4 (i 4) (5 x^{6})^{(4 - i)} (2 x^{3})^{i}

Erweitere Summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (5 x^{6})^{4} (2 x^{3})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (5 x^{6})^{3} (2 x^{3})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (5 x^{6})^{2} (2 x^{3})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (5 x^{6})^{1} (2 x^{3})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (5 x^{6})^{0} (2 x^{3})^{4}

Vereinfache

\frac{4 !}{0 ! ( 4 - 0 ) !} (5 x^{6})^{4} (2 x^{3})^{0} : 625 x^{24}

Vereinfache

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 x^{6})^{3} (2 x^{3})^{1} : 1000 x^{21}

Vereinfache

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 x^{6})^{2} (2 x^{3})^{2} : 600 x^{18}

Vereinfache

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 x^{6})^{1} (2 x^{3})^{3} : 160 x^{15}

Vereinfache

\frac{4 !}{4 ! ( 4 - 4 ) !} (5 x^{6})^{0} (2 x^{3})^{4} : 16 x^{12}

= 625 x^{24} + 1000 x^{21} + 600 x^{18} + 160 x^{15} + 16 x^{12}

p a r i t y f (x) = x e^{x} csc (x)

\int_{- \infty}^{0} x e^{- x} d x

t an g e n t y = 5 x, (5, 5)

d er i v a t i v e x - x^{2}

(4 t)^{^{'}}