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

The solution to (x-2y)^3-(x+2y)^3 is -12x^2y-16y^3

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

simplify

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

- 12 x^{2} y - 16 y^{3}

Solution steps

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

Group like terms

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

Add similar elements:

x^{3} - x^{3} = 0

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

Add similar elements:

- 6 x^{2} y - 6 x^{2} y = - 12 x^{2} y

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

Add similar elements:

12 x y^{2} - 12 x y^{2} = 0

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

Add similar elements:

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

= - 12 x^{2} y - 16 y^{3}

6 x + 24 y - 18

n^{2} - 4 n + (- 12)

a^{2} \cdot b^{4} + a^{4} \cdot b^{2}

(x + 1) 2 + (x - 1) 2

[\frac{( 81 y ^{8} )}{( 16 x ^{4} )}]^{\frac{3}{4}}