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

Options

A. `250y^(3)+120x^(2)y`
B. `250y^(3)-120x^(2)y`
C. `-250y^(3)-120x^(2)y`
D. `-250y^(3)+120x^(2)y`

Answer

C

Explanation

`(2x-5y)^(3)-(2x+5y)^(3)=[(2x)^(3)-(5y)^(3)-3(2x)(5y)(2x-5y)]-[(2x)^(3)+(5y)^(3)+3(2x)(5y)(2x+5y)]`
`["using identity",(a-b)^(3)=a^(3)-b^(3)-3ab (a-b)and (a+b)^(3)=a^(3)=b^(3)+3ab(a+b)]`
`=(2x)^(3)-(5y)^(3)-30xy(2x-5y)-(2x)^(3)-(5y)^(3)-30xy(2x+5y)`
`=-2(5y)^(3)-30xy(2x-5y+2x+5y)`
`=-2xx125y^(3) (4x)=-250y^(3)-120x^(2)y`