What is (x+y)^3+(x-2y)^3 ?

The solution to (x+y)^3+(x-2y)^3 is 2x^3-3x^2y+15xy^2-7y^3

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simplify (x+y)^3+(x-2y)^3

simplify

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

2 x^{3} - 3 x^{2} y + 15 x y^{2} - 7 y^{3}

Solution steps

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

Expand

(x - 2 y)^{3} : x^{3} - 6 x^{2} y + 12 x y^{2} - 8 y^{3}

= x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} + x^{3} - 6 x^{2} y + 12 x y^{2} - 8 y^{3}

Group like terms

= x^{3} + x^{3} + 3 x^{2} y - 6 x^{2} y + 3 x y^{2} + 12 x y^{2} + y^{3} - 8 y^{3}

Add similar elements:

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

= 2 x^{3} + 3 x^{2} y - 6 x^{2} y + 3 x y^{2} + 12 x y^{2} + y^{3} - 8 y^{3}

Add similar elements:

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

= 2 x^{3} - 3 x^{2} y + 3 x y^{2} + 12 x y^{2} + y^{3} - 8 y^{3}

Add similar elements:

3 x y^{2} + 12 x y^{2} = 15 x y^{2}

= 2 x^{3} - 3 x^{2} y + 15 x y^{2} + y^{3} - 8 y^{3}

Add similar elements:

y^{3} - 8 y^{3} = - 7 y^{3}

= 2 x^{3} - 3 x^{2} y + 15 x y^{2} - 7 y^{3}

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What is (x+y)^3+(x-2y)^3 ?
The solution to (x+y)^3+(x-2y)^3 is 2x^3-3x^2y+15xy^2-7y^3