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

The solution to (a+b)^2(a-b)^3-2a^3 is a^5-b^5-2a^3b^2-b^3a^2-a^4b+3a^2b^3+ab^4-2a^3

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simplify (a+b)^2(a-b)^3-2a^3

simplify

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

a^{5} - b^{5} - 2 a^{3} b^{2} - b^{3} a^{2} - a^{4} b + 3 a^{2} b^{3} + a b^{4} - 2 a^{3}

Solution steps

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

Expand

(a + b)^{2} : a^{2} + 2 ab + b^{2}

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

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

Expand

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

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

Distribute parentheses

= a^{3} a^{2} + a^{3} \cdot 2 ab + a^{3} b^{2} - 3 a^{2} b a^{2} - 3 a^{2} b \cdot 2 ab - 3 a^{2} b b^{2} + 3 a b^{2} a^{2} + 3 a b^{2} \cdot 2 ab + 3 a b^{2} b^{2} - b^{3} a^{2} - b^{3} \cdot 2 ab - b^{3} b^{2} - 2 a^{3}

Simplify

a^{3} a^{2} + a^{3} \cdot 2 ab + a^{3} b^{2} - 3 a^{2} b a^{2} - 3 a^{2} b \cdot 2 ab - 3 a^{2} b b^{2} + 3 a b^{2} a^{2} + 3 a b^{2} \cdot 2 ab + 3 a b^{2} b^{2} - b^{3} a^{2} - b^{3} \cdot 2 ab - b^{3} b^{2} : a^{5} - b^{5} - 2 a^{3} b^{2} - b^{3} a^{2} - a^{4} b + 3 a^{2} b^{3} + a b^{4}

= a^{5} - b^{5} - 2 a^{3} b^{2} - b^{3} a^{2} - a^{4} b + 3 a^{2} b^{3} + a b^{4} - 2 a^{3}

(36 x^{2})^{\frac{1}{2}}

2 (sin (x) - cos (x)) - (sin (2 x) - cos (2 x))

(w^{4})^{3}

\frac{( 5 x ^{2} + 4 x ^{2} + 3 x )}{( + x )}

\frac{w}{0.1 n ^{2}}

What is (a+b)^2(a-b)^3-2a^3 ?
The solution to (a+b)^2(a-b)^3-2a^3 is a^5-b^5-2a^3b^2-b^3a^2-a^4b+3a^2b^3+ab^4-2a^3