erweitern (2x-4)(2x^2-8x+35)^4dx

Lösung

erweitern

(2 x - 4) (2 x^{2} - 8 x + 35)^{4} d x

32 x^{9} d x - 576 x^{8} d x + 6336 x^{7} d x - 45696 x^{6} d x + 244656 x^{5} d x - 962784 x^{4} d x + 2854320 x^{3} d x - 5997600 x^{2} d x + 8489250 x d x - 6002500 d x

Schritte zur Lösung

(2 x - 4) (2 x^{2} - 8 x + 35)^{4} d x

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = (2 x^{2} - 8 x + 35)^{4} d x, b = 2 x, c = 4

= (2 x^{2} - 8 x + 35)^{4} d x \cdot 2 x - (2 x^{2} - 8 x + 35)^{4} d x \cdot 4

= 2 x (2 x^{2} - 8 x + 35)^{4} d x - 4 (2 x^{2} - 8 x + 35)^{4} d x

Vereinfache

2 x (2 x^{2} - 8 x + 35)^{4} d x - 4 (2 x^{2} - 8 x + 35)^{4} d x : 32 x^{9} d x - 576 x^{8} d x + 6336 x^{7} d x - 45696 x^{6} d x + 244656 x^{5} d x - 962784 x^{4} d x + 2854320 x^{3} d x - 5997600 x^{2} d x + 8489250 x d x - 6002500 d x

= 32 x^{9} d x - 576 x^{8} d x + 6336 x^{7} d x - 45696 x^{6} d x + 244656 x^{5} d x - 962784 x^{4} d x + 2854320 x^{3} d x - 5997600 x^{2} d x + 8489250 x d x - 6002500 d x

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e x p an d \frac{x ^{2} - 10 x - 41}{( x + 1 ) ( x + 4 ) ( x - 1 )}

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e x p an d \frac{5 ( x - 1 ) ^{4} ( x ^{2} + x + 1 ) ^{4} ( x ^{3} + 2 )}{x ^{11}}

s im pl i f y (- 1 + i)^{17}