erweitern (x-y)^2((x-y)-Δ)

Lösung

erweitern

(x - y)^{2} ((x - y) - Δ)

x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} - Δ x^{2} + 2Δ x y - Δ y^{2}

Schritte zur Lösung

(x - y)^{2} ((x - y) - Δ)

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = (x - y)^{2}, b = (x - y), c = Δ

= (x - y)^{2} (x - y) - (x - y)^{2} Δ

= (x - y)^{2} (x - y) - Δ (x - y)^{2}

Vereinfache

(x - y)^{2} (x - y) - Δ (x - y)^{2} : x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} - Δ x^{2} + 2Δ x y - Δ y^{2}

= x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} - Δ x^{2} + 2Δ x y - Δ y^{2}

e x p an d 2 u y^{2} (y d u + u d y) + (y^{2} - 3 y^{2} v^{2}) d u

e x p an d, (x - 1) (x - 2) (x - 4)

e x p an d (p + Δ p + 1)^{2}

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

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