Question

Simplify of the following:

(2x − 5y)³ − (2x + 5y)³

Answer 1

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`.