What is (2x-5y)^3-(2x+5y)^3 ?

The solution to (2x-5y)^3-(2x+5y)^3 is -120x^2y-250y^3

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simplify (2x-5y)^3-(2x+5y)^3

simplify

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

- 120 x^{2} y - 250 y^{3}

Solution steps

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

Expand

(2 x - 5 y)^{3} : 8 x^{3} - 60 x^{2} y + 150 x y^{2} - 125 y^{3}

= 8 x^{3} - 60 x^{2} y + 150 x y^{2} - 125 y^{3} - (2 x + 5 y)^{3}

Expand

- (2 x + 5 y)^{3} : - 8 x^{3} - 60 x^{2} y - 150 x y^{2} - 125 y^{3}

= 8 x^{3} - 60 x^{2} y + 150 x y^{2} - 125 y^{3} - 8 x^{3} - 60 x^{2} y - 150 x y^{2} - 125 y^{3}

Group like terms

= 8 x^{3} - 8 x^{3} - 60 x^{2} y - 60 x^{2} y + 150 x y^{2} - 150 x y^{2} - 125 y^{3} - 125 y^{3}

Add similar elements:

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

= - 60 x^{2} y - 60 x^{2} y + 150 x y^{2} - 150 x y^{2} - 125 y^{3} - 125 y^{3}

Add similar elements:

- 60 x^{2} y - 60 x^{2} y = - 120 x^{2} y

= - 120 x^{2} y + 150 x y^{2} - 150 x y^{2} - 125 y^{3} - 125 y^{3}

Add similar elements:

150 x y^{2} - 150 x y^{2} = 0

= - 120 x^{2} y - 125 y^{3} - 125 y^{3}

Add similar elements:

- 125 y^{3} - 125 y^{3} = - 250 y^{3}

= - 120 x^{2} y - 250 y^{3}

2 x \cdot 5. 5^{2}

x^{1} + x^{2} + x^{3}

(2 x + 5)^{6}

x^{4} + 324

27 m^{6} + 729 y^{12}

What is (2x-5y)^3-(2x+5y)^3 ?
The solution to (2x-5y)^3-(2x+5y)^3 is -120x^2y-250y^3