# Simplify of the Following: (2x − 5y)3 − (2x + 5y)3 - Mathematics

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)^3is  -120x^2y - 250y^3.

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.3 | Q 17.4 | Page 20

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