What is (x-y)^3-(x+y)^3 ?

The solution to (x-y)^3-(x+y)^3 is -6x^2y-2y^3

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simplify (x-y)^3-(x+y)^3

simplify

(x - y)^{3} - (x + y)^{3}

- 6 x^{2} y - 2 y^{3}

Solution steps

(x - y)^{3} - (x + y)^{3}

Expand

(x - y)^{3} : x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}

= x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} - (x + y)^{3}

Expand

- (x + y)^{3} : - x^{3} - 3 x^{2} y - 3 x y^{2} - y^{3}

= x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} - x^{3} - 3 x^{2} y - 3 x y^{2} - y^{3}

Group like terms

= x^{3} - x^{3} - 3 x^{2} y - 3 x^{2} y + 3 x y^{2} - 3 x y^{2} - y^{3} - y^{3}

Add similar elements:

x^{3} - x^{3} = 0

= - 3 x^{2} y - 3 x^{2} y + 3 x y^{2} - 3 x y^{2} - y^{3} - y^{3}

Add similar elements:

- 3 x^{2} y - 3 x^{2} y = - 6 x^{2} y

= - 6 x^{2} y + 3 x y^{2} - 3 x y^{2} - y^{3} - y^{3}

Add similar elements:

3 x y^{2} - 3 x y^{2} = 0

= - 6 x^{2} y - y^{3} - y^{3}

Add similar elements:

- y^{3} - y^{3} = - 2 y^{3}

= - 6 x^{2} y - 2 y^{3}

(3 x y - 2 y)^{3}

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