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

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

Text Solution

Verified by Experts

Putting `2x=a and 5y=b`, we get
`(2x-5y)^3-(2x+5y)^3`
`=(a-b)^3-(a+b)^3`
`={a^3-b^3)-3ab(a-b)}-{a^3+b^3+3ab(a+b)}`
`=(a^3-b^3-3a^2 b+3ab^2-a^3-b^3-3a^2b-3ab^2)`
`=-2b^3-6a^2 b=-2xx(5y)^3-6xx(2x)^2xx(5y)`
`=(-2xx125y^3)-(6xx4x^2xx5y)=-250y^3-120x^2 y`.
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