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

The solution to (4x+2y)^3-(4x-2y)^3 is 192x^2y+16y^3

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

simplify

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

192 x^{2} y + 16 y^{3}

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} = 0

= 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 = 192 x^{2} y

= 192 x^{2} y + 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} = 0

= 192 x^{2} y + 8 y^{3} + 8 y^{3}

Add similar elements:

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

= 192 x^{2} y + 16 y^{3}

(8 x - 3) (2 x - 5) - (3 x - 8) (x - 5)

(- 2 y^{- 3} z^{6})^{3}

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(3 x + 8)^{5}

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What is (4x+2y)^3-(4x-2y)^3 ?
The solution to (4x+2y)^3-(4x-2y)^3 is 192x^2y+16y^3