erweitern z(x^2-xy+y^2)^4

Lösung

erweitern

z (x^{2} - x y + y^{2})^{4}

z x^{8} - 4 z x^{7} y + 10 z x^{6} y^{2} - 16 z x^{5} y^{3} + 19 z x^{4} y^{4} - 16 z x^{3} y^{5} + 10 z x^{2} y^{6} - 4 z x y^{7} + z y^{8}

Schritte zur Lösung

z (x^{2} - x y + y^{2})^{4}

(x^{2} - x y + y^{2})^{4} = x^{8} - 4 x^{7} y + 10 x^{6} y^{2} - 16 x^{5} y^{3} + 19 x^{4} y^{4} - 16 x^{3} y^{5} + 10 x^{2} y^{6} - 4 x y^{7} + y^{8}

= z (x^{8} - 4 x^{7} y + 10 x^{6} y^{2} - 16 x^{5} y^{3} + 19 x^{4} y^{4} - 16 x^{3} y^{5} + 10 x^{2} y^{6} - 4 x y^{7} + y^{8})

Setze Klammern

= z x^{8} + z (- 4 x^{7} y) + z \cdot 10 x^{6} y^{2} + z (- 16 x^{5} y^{3}) + z \cdot 19 x^{4} y^{4} + z (- 16 x^{3} y^{5}) + z \cdot 10 x^{2} y^{6} + z (- 4 x y^{7}) + z y^{8}

Wende Minus-Plus Regeln an

+ (- a) = - a

= z x^{8} - 4 z x^{7} y + 10 z x^{6} y^{2} - 16 z x^{5} y^{3} + 19 z x^{4} y^{4} - 16 z x^{3} y^{5} + 10 z x^{2} y^{6} - 4 z x y^{7} + z y^{8}

e x p an d \frac{y ( y + 5 )}{2 y - 3}

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

e x p an d \frac{1 - x}{z ( 5 - x )}

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

e x p an d - ((- 10, - 4, - 2) + (4, 3, 5))