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Question
Simplify of the following:
(2x − 5y)3 − (2x + 5y)3
Solution
In the given problem, we have to simplify equation
Given (2x − 5y)3 − (2x + 5y)3
We shall use the identity `a^3 - b^3 = (a-b)(a^2+ b^2 + ab)`
Here ` a= (2x - 5y), b = (2x + 5y)`
By applying the identity we get
` = (2x - 5y - 2x 5y)[(2x - 5y)^2 +(2x + 5y)^2 + ((2x - 5y) xx (2x + 5y))]`
` = ( 2x - 5y - 2x - 5y)[(2x xx 2x + 5y xx 5y - 2 xx 2x xx 5y) + (2x xx 2x + 5yxx 5y + 2 xx 2x xx 5y) + ( 4x^2 - 25y^2)]`
` = ( - 10y)[(4x^2 + 25y^2 - 20xy)+ (4x^2 + 25y^2 + 20xy ) + 4x^2 + 25y^2 ]`
` = ( - 10y)[4x^2 + 25y^2 - 20xy+ 4x^2 + 25y^2 + 20xy + 4x^2 -25y^2 ]`
By rearranging the variable we get,
` = ( - 10y)[4x^2 + 4x^2 + 4x^2 + 25y^2]`
` = - 10y xx [12x^2 + 25y^2]`
`= -120x^2y - 250y^3`
Hence the simplified value of `2x - 5y^3 -(2x + 5y)^3`is `-120x^2y - 250y^3`.
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