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

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

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

simplify

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

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

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} = 0

= - 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 = - 6 a^{2} b

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

Add similar elements:

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

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

Add similar elements:

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

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

8 x - 4 y + 12 z

(4 x + 5 y)^{3}

x^{2} - 3 2 x + 12

(\frac{x + 1}{2})^{3}

(4 - y)^{3}