Simplify `(2x-5y)^(3)-(2x+5y)^(3)`.

Options

A. `120x^(2)y-250y^(3)`
B. `120x^(2)y+250y^(3)`
C. `-120x^(2)y-250y^(3)`
D. can not determine its value

Answer

C

Explanation

We have, `(2x-5y)^(3)-(2x+5y)^(3)`
`={(2x-5y)-(2x+5y)}{(2x-5y)^(2)+(2x-5y)(2x+5y)+(2x+5y)^(2)} " " [because a^(3)-b^(3)=(a-b)(a^(2)+ab+b^(2))]`
`=(2x-5y-2x-5y)(4x^(2)+25y^(2)-20xy+4x^(2)-25y^(2)_25y^(2)+20xy)`
`=(-10y)(2x^(2)+25y^(2))=-120x^(2)y-250y^(3)`