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

The solution to (a-b)^3+(a+b)^3 is 2a^3+6ab^2

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

simplify

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

2 a^{3} + 6 a b^{2}

Solution steps

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

- 3 a^{2} b + 3 a^{2} b = 0

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

Add similar elements:

3 a b^{2} + 3 a b^{2} = 6 a b^{2}

= 2 a^{3} + 6 a b^{2} - b^{3} + b^{3}

Add similar elements:

- b^{3} + b^{3} = 0

= 2 a^{3} + 6 a b^{2}

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