What is (4x+2y)^3+(4x-2y)^3 ?

The solution to (4x+2y)^3+(4x-2y)^3 is 128x^3+96xy^2

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simplify (4x+2y)^3+(4x-2y)^3

simplify

(4 x + 2 y)^{3} + (4 x - 2 y)^{3}

128 x^{3} + 96 x y^{2}

Solution steps

(4 x + 2 y)^{3} + (4 x - 2 y)^{3}

Expand

(4 x + 2 y)^{3} : 64 x^{3} + 96 x^{2} y + 48 x y^{2} + 8 y^{3}

= 64 x^{3} + 96 x^{2} y + 48 x y^{2} + 8 y^{3} + (4 x - 2 y)^{3}

Expand

(4 x - 2 y)^{3} : 64 x^{3} - 96 x^{2} y + 48 x y^{2} - 8 y^{3}

= 64 x^{3} + 96 x^{2} y + 48 x y^{2} + 8 y^{3} + 64 x^{3} - 96 x^{2} y + 48 x y^{2} - 8 y^{3}

Group like terms

= 64 x^{3} + 64 x^{3} + 96 x^{2} y - 96 x^{2} y + 48 x y^{2} + 48 x y^{2} + 8 y^{3} - 8 y^{3}

Add similar elements:

64 x^{3} + 64 x^{3} = 128 x^{3}

= 128 x^{3} + 96 x^{2} y - 96 x^{2} y + 48 x y^{2} + 48 x y^{2} + 8 y^{3} - 8 y^{3}

Add similar elements:

96 x^{2} y - 96 x^{2} y = 0

= 128 x^{3} + 48 x y^{2} + 48 x y^{2} + 8 y^{3} - 8 y^{3}

Add similar elements:

48 x y^{2} + 48 x y^{2} = 96 x y^{2}

= 128 x^{3} + 96 x y^{2} + 8 y^{3} - 8 y^{3}

Add similar elements:

8 y^{3} - 8 y^{3} = 0

= 128 x^{3} + 96 x y^{2}

\frac{- 4}{x}

(\frac{x - 1}{x})^{2}

- d (d - 2) - d (d + 3)

\frac{( 3 ^{n + 1} + 3 ^{n} )}{( 3 ^{n + 3} - 3 ^{n + 1} )}

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

What is (4x+2y)^3+(4x-2y)^3 ?
The solution to (4x+2y)^3+(4x-2y)^3 is 128x^3+96xy^2