What is 27(x+y)^3-8(x-y)^3 ?

The solution to 27(x+y)^3-8(x-y)^3 is 19x^3+105x^2y+57xy^2+35y^3

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simplify 27(x+y)^3-8(x-y)^3

simplify

27 (x + y)^{3} - 8 (x - y)^{3}

19 x^{3} + 105 x^{2} y + 57 x y^{2} + 35 y^{3}

Solution steps

27 (x + y)^{3} - 8 (x - y)^{3}

Expand

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

= 27 x^{3} + 81 x^{2} y + 81 x y^{2} + 27 y^{3} - 8 (x - y)^{3}

Expand

- 8 (x - y)^{3} : - 8 x^{3} + 24 x^{2} y - 24 x y^{2} + 8 y^{3}

= 27 x^{3} + 81 x^{2} y + 81 x y^{2} + 27 y^{3} - 8 x^{3} + 24 x^{2} y - 24 x y^{2} + 8 y^{3}

Group like terms

= 27 x^{3} - 8 x^{3} + 81 x^{2} y + 24 x^{2} y + 81 x y^{2} - 24 x y^{2} + 27 y^{3} + 8 y^{3}

Add similar elements:

27 x^{3} - 8 x^{3} = 19 x^{3}

= 19 x^{3} + 81 x^{2} y + 24 x^{2} y + 81 x y^{2} - 24 x y^{2} + 27 y^{3} + 8 y^{3}

Add similar elements:

81 x^{2} y + 24 x^{2} y = 105 x^{2} y

= 19 x^{3} + 105 x^{2} y + 81 x y^{2} - 24 x y^{2} + 27 y^{3} + 8 y^{3}

Add similar elements:

81 x y^{2} - 24 x y^{2} = 57 x y^{2}

= 19 x^{3} + 105 x^{2} y + 57 x y^{2} + 27 y^{3} + 8 y^{3}

Add similar elements:

27 y^{3} + 8 y^{3} = 35 y^{3}

= 19 x^{3} + 105 x^{2} y + 57 x y^{2} + 35 y^{3}

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What is 27(x+y)^3-8(x-y)^3 ?
The solution to 27(x+y)^3-8(x-y)^3 is 19x^3+105x^2y+57xy^2+35y^3