# Simplify of the Following: ( X + 2 X ) 3 + ( X − 2 X ) 3 - Mathematics

Simplify of the following:

$\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3$

#### Solution

In the given problem, we have to simplify equation

Given  (x+ 2/x)^3 + (x-2/x)

We shall use the identity  a^3 + b^3 = (a+b)(a^2 +b^2 - ab)

Here  a= (x+2/x) ,b=(x-2/x)

By applying identity we get

 = (x+2/x + x - 2/x-2/x) [(x+2/x)^2 + (x-2/x)^2 - ((x+2/x)  xx (x-2/x))]

 = (x+2/x + x -2/x) [(x  xx x + 2/x xx 2/x + 2  xx x xx 2/x) +(x  xx x + 2/x xx 2/x - 2  xx x xx 2/x) - (x^2 + 4/x^2)]

 = (2x)[(x^2 + 4/x^2 +(4x)/x)+ (x^2 + 4/x^2 -(4x)/x) - (x^2 - 4/x^2)]

 = (2x)[x^2+ 4/x^2 + (4x)/x + x^2 +  4 /x^2 -(4x)/x - x^2 + 4 /x^2]

By rearranging the variable we get,

 = (2x)[x^2 + 4/x^2 + 4/x^2 + 4/x^2]

 = 2x xx [x^2+ 12/x^2]

 = 2x^3 + 24/x

Hence the simplified value of (x+2/x)^3+(x-2/x)^3is 2x^3 + 24/x.

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.3 | Q 17.3 | Page 20