What is (x+y)^3-27(x-y)^3 ?

The solution to (x+y)^3-27(x-y)^3 is -26x^3+84x^2y-78xy^2+28y^3

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simplify (x+y)^3-27(x-y)^3

simplify

(x + y)^{3} - 27 (x - y)^{3}

- 26 x^{3} + 84 x^{2} y - 78 x y^{2} + 28 y^{3}

Solution steps

(x + y)^{3} - 27 (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} - 27 (x - y)^{3}

Expand

- 27 (x - y)^{3} : - 27 x^{3} + 81 x^{2} y - 81 x y^{2} + 27 y^{3}

= x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - 27 x^{3} + 81 x^{2} y - 81 x y^{2} + 27 y^{3}

Group like terms

= x^{3} - 27 x^{3} + 3 x^{2} y + 81 x^{2} y + 3 x y^{2} - 81 x y^{2} + y^{3} + 27 y^{3}

Add similar elements:

x^{3} - 27 x^{3} = - 26 x^{3}

= - 26 x^{3} + 3 x^{2} y + 81 x^{2} y + 3 x y^{2} - 81 x y^{2} + y^{3} + 27 y^{3}

Add similar elements:

3 x^{2} y + 81 x^{2} y = 84 x^{2} y

= - 26 x^{3} + 84 x^{2} y + 3 x y^{2} - 81 x y^{2} + y^{3} + 27 y^{3}

Add similar elements:

3 x y^{2} - 81 x y^{2} = - 78 x y^{2}

= - 26 x^{3} + 84 x^{2} y - 78 x y^{2} + y^{3} + 27 y^{3}

Add similar elements:

y^{3} + 27 y^{3} = 28 y^{3}

= - 26 x^{3} + 84 x^{2} y - 78 x y^{2} + 28 y^{3}

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What is (x+y)^3-27(x-y)^3 ?
The solution to (x+y)^3-27(x-y)^3 is -26x^3+84x^2y-78xy^2+28y^3