What is (2x+y)^3+8(x+y)^3 ?

The solution to (2x+y)^3+8(x+y)^3 is 16x^3+36x^2y+30xy^2+9y^3

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simplify (2x+y)^3+8(x+y)^3

simplify

(2 x + y)^{3} + 8 (x + y)^{3}

16 x^{3} + 36 x^{2} y + 30 x y^{2} + 9 y^{3}

Solution steps

(2 x + y)^{3} + 8 (x + y)^{3}

Expand

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

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

= 8 x^{3} + 12 x^{2} y + 6 x y^{2} + y^{3} + 8 x^{3} + 24 x^{2} y + 24 x y^{2} + 8 y^{3}

Group like terms

= 8 x^{3} + 8 x^{3} + 12 x^{2} y + 24 x^{2} y + 6 x y^{2} + 24 x y^{2} + y^{3} + 8 y^{3}

Add similar elements:

8 x^{3} + 8 x^{3} = 16 x^{3}

= 16 x^{3} + 12 x^{2} y + 24 x^{2} y + 6 x y^{2} + 24 x y^{2} + y^{3} + 8 y^{3}

Add similar elements:

12 x^{2} y + 24 x^{2} y = 36 x^{2} y

= 16 x^{3} + 36 x^{2} y + 6 x y^{2} + 24 x y^{2} + y^{3} + 8 y^{3}

Add similar elements:

6 x y^{2} + 24 x y^{2} = 30 x y^{2}

= 16 x^{3} + 36 x^{2} y + 30 x y^{2} + y^{3} + 8 y^{3}

Add similar elements:

y^{3} + 8 y^{3} = 9 y^{3}

= 16 x^{3} + 36 x^{2} y + 30 x y^{2} + 9 y^{3}

\frac{( - 32 x ^{5} + 24 x ^{4} - 56 x ^{3} )}{( - 8 x ^{4} )}

(\frac{2 x - 2}{x})^{3}

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

(3 m^{2} + 5 n^{2})^{3}

a^{3} - 27 b^{3}

What is (2x+y)^3+8(x+y)^3 ?
The solution to (2x+y)^3+8(x+y)^3 is 16x^3+36x^2y+30xy^2+9y^3