erweitern (x-y)^3+(x-y)^2+(x-y)

Lösung

erweitern

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

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

Schritte zur Lösung

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

Apply rule:

a + (b + c) = a + b + c

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

= (x - y)^{3} + (x - y)^{2} + x - y

Schreibe

(x - y)^{3}

um:

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

= x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} + (x - y)^{2} + x - y

Schreibe

(x - y)^{2}

um:

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

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

s im pl i f y \frac{( 4 a ^{4} - 8 a ^{2} \cdot b ^{2} + 4 b ^{4} )}{( a ^{2} \cdot b - b ^{3} )}

s im pl i f y (3 + 8) \cdot x^{6} - 42 - 7

f a c t or x^{7} y^{7} - x y

f a c t or 2 x^{2} - 3 x y - 2 y^{2}

e x p an d (x - y)^{10}