erweitern (a+b)sqrt(a^3-a^2b+ab^2)

Lösung

erweitern

(a + b) a^{3} - a^{2} b + a b^{2}

a a^{3} - a^{2} b + a b^{2} + b a^{3} - a^{2} b + a b^{2}

Schritte zur Lösung

(a + b) a^{3} - a^{2} b + a b^{2}

= a^{3} - a^{2} b + a b^{2} (a + b)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a^{3} - a^{2} b + a b^{2} (a + b) = a^{3} - a^{2} b + a b^{2} a + a^{3} - a^{2} b + a b^{2} b

= a^{3} - a^{2} b + a b^{2} a + a^{3} - a^{2} b + a b^{2} b

= a a^{3} - a^{2} b + a b^{2} + b a^{3} - a^{2} b + a b^{2}

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

e x p an d \frac{- S ^{3} - S}{4 ( S ^{4} + S ^{2} + 4 )}

e x p an d (x^{2} - x - e^{3 x})^{2}

s im pl i f y (x + 2 x) (x - 2 x)

s im pl i f y (e^{iπ x} - e^{- iπ x})^{2}