erweitern x(x^2-2x+2)^2

Lösung

erweitern

x (x^{2} - 2 x + 2)^{2}

x^{5} - 4 x^{4} + 8 x^{3} - 8 x^{2} + 4 x

Schritte zur Lösung

x (x^{2} - 2 x + 2)^{2}

(x^{2} - 2 x + 2)^{2} = x^{4} - 4 x^{3} + 8 x^{2} - 8 x + 4

= x (x^{4} - 4 x^{3} + 8 x^{2} - 8 x + 4)

Setze Klammern

= x x^{4} + x (- 4 x^{3}) + x \cdot 8 x^{2} + x (- 8 x) + x \cdot 4

Wende Minus-Plus Regeln an

+ (- a) = - a

= x^{4} x - 4 x^{3} x + 8 x^{2} x - 8 xx + 4 x

Vereinfache

x^{4} x - 4 x^{3} x + 8 x^{2} x - 8 xx + 4 x : x^{5} - 4 x^{4} + 8 x^{3} - 8 x^{2} + 4 x

= x^{5} - 4 x^{4} + 8 x^{3} - 8 x^{2} + 4 x

e x p an d R e ((1 + j) (2 - 3 j))

e x p an d (t - 1) e^{t}

e x p an d \frac{9 ( 2 15 - 5 )}{10}

e x p an d 2 x H (x - 2)

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