Question

Factorize the following expressions: 

( x + 2)³ + ( x - 2)³

Answer 1

`= (x + 2 + x - 2)((x + 2^2 -(x + 2)(x - 2) + (x - 2)^2)     [∵ a^3 + b^3 = (a + b)(a^2 - ab + b^2)]`

`= 2x(x^2 + 4x + 4 - (x + 2)(x - 2) + x^2 - 4x + 4)       [∵ (a + b)^2 = a^2 + 2ab + b^2, (a - b)^2 = a^2 - 2ab + b^2]`

`= 2x (2x^2 + 8 - (x^2 - 2^2))`       `[∵ (a + b)(a - b) = a^2 - b^2]`

`=2x(2x^2 + 8 - x^2 + 4)`

`= 2x(x^2 + 12)`

`∴ (x + 2)^3 + (x - 2)^3 = 2x(x^2 + 12)`