erweitern (2x^3-4x^2+1)^5

Lösung

erweitern

(2 x^{3} - 4 x^{2} + 1)^{5}

32 x^{15} - 320 x^{14} + 1280 x^{13} - 2480 x^{12} + 1920 x^{11} + 896 x^{10} - 2480 x^{9} + 800 x^{8} + 960 x^{7} - 600 x^{6} - 160 x^{5} + 160 x^{4} + 10 x^{3} - 20 x^{2} + 1

Schritte zur Lösung

(2 x^{3} - 4 x^{2} + 1)^{5}

(2 x^{3} - 4 x^{2} + 1)^{5} = (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1)

= (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1)

Multipliziere aus

(2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) (2 x^{3} - 4 x^{2} + 1) : 32 x^{15} - 320 x^{14} + 1280 x^{13} - 2480 x^{12} + 1920 x^{11} + 896 x^{10} - 2480 x^{9} + 800 x^{8} + 960 x^{7} - 600 x^{6} - 160 x^{5} + 160 x^{4} + 10 x^{3} - 20 x^{2} + 1

= 32 x^{15} - 320 x^{14} + 1280 x^{13} - 2480 x^{12} + 1920 x^{11} + 896 x^{10} - 2480 x^{9} + 800 x^{8} + 960 x^{7} - 600 x^{6} - 160 x^{5} + 160 x^{4} + 10 x^{3} - 20 x^{2} + 1

e x p an d π (4 x - 3)^{2}

e x p an d (x + 1) \cdot e^{- x} + 2

e x p an d π (2 ln^{2} (2) - 2 (2 ln (2) - 2))

e x p an d \frac{x d x}{( x - 2 ) ( x ^{2} - 1 )}

e x p an d - 3^{4}