Question

Simplify of the following:

(x+3)³ + (x−3)³

Answer 1

In the given problem, we have to simplify equation 

Given  (x+3)³ + (x−3)³

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

Here  `a= (x+3),b= (x-3)`

By applying identity we get 

` = (x+ 3+x - 3)[(x+ 3)^2 + (x-3)^2 - (x+ 3)(x-3)]`

` = 2x[(x^2 + 3^2 + 2 xx x xx 3) + (x^2 + 3^2 - 2 xx x xx 3) -(x^2-3^2)]`

`  = 2x [(x^2+ 9 + 6x) + (x^2 + 9 - 6 x)-(x^2 - 3^2)]`

` = 2x[x^2 + 9 + 6x + x^2 + 9 -6x - x^2 + 9]`

`= 2x [x^2 + x^2 - x^2 - 6x + 6x+ 9 + 9 + 9]`

` = 2x [x^2 + 27]`

` = 2x^3 + 54x`

Hence simplified form of expression`(x+3)^3 +(x-3)^3`is  `2x^3 + 54x`.