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

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

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

simplify

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

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

Solution steps

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

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

Expand

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

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

Expand

3 a (a - b)^{2} (a + b) : 3 a^{4} - 3 a^{3} b - 3 a^{2} b^{2} + 3 a b^{3}

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

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