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

The solution to (2x+3y)^3-(2x-3y)^3 is 72x^2y+54y^3

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

simplify

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

72 x^{2} y + 54 y^{3}

Solution steps

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

Expand

(2 x + 3 y)^{3} : 8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}

= 8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} - (2 x - 3 y)^{3}

Expand

- (2 x - 3 y)^{3} : - 8 x^{3} + 36 x^{2} y - 54 x y^{2} + 27 y^{3}

= 8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} - 8 x^{3} + 36 x^{2} y - 54 x y^{2} + 27 y^{3}

Group like terms

= 8 x^{3} - 8 x^{3} + 36 x^{2} y + 36 x^{2} y + 54 x y^{2} - 54 x y^{2} + 27 y^{3} + 27 y^{3}

Add similar elements:

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

= 36 x^{2} y + 36 x^{2} y + 54 x y^{2} - 54 x y^{2} + 27 y^{3} + 27 y^{3}

Add similar elements:

36 x^{2} y + 36 x^{2} y = 72 x^{2} y

= 72 x^{2} y + 54 x y^{2} - 54 x y^{2} + 27 y^{3} + 27 y^{3}

Add similar elements:

54 x y^{2} - 54 x y^{2} = 0

= 72 x^{2} y + 27 y^{3} + 27 y^{3}

Add similar elements:

27 y^{3} + 27 y^{3} = 54 y^{3}

= 72 x^{2} y + 54 y^{3}

(5 x^{2} + 7 y^{3})^{3}

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

\frac{x ^{2} \cdot 1}{3 ( x ^{5} )}

2 cos^{2} (5 x) - 1

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

What is (2x+3y)^3-(2x-3y)^3 ?
The solution to (2x+3y)^3-(2x-3y)^3 is 72x^2y+54y^3