What is expand (a+b)sqrt(a^3-a^2b+ab^2) ?

The solution to expand (a+b)sqrt(a^3-a^2b+ab^2) is asqrt(a^3-a^2b+ab^2)+bsqrt(a^3-a^2b+ab^2)

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

expand

(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}

Solution steps

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

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

Apply the distributive law:

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}

\frac{sin ^{2} ( x ) ( 1 + cos ( x ) )}{1 - cos ( x )}

\frac{- S ^{3} - S}{4 ( S ^{4} + S ^{2} + 4 )}

f (x) = (x^{2} - x - e^{3 x})^{2}

(x + 2 x) (x - 2 x)

\frac{d}{d x} ((e^{iπ x} - e^{- iπ x})^{2})

What is expand (a+b)sqrt(a^3-a^2b+ab^2) ?
The solution to expand (a+b)sqrt(a^3-a^2b+ab^2) is asqrt(a^3-a^2b+ab^2)+bsqrt(a^3-a^2b+ab^2)