Question

Factorise (x+2)^3-(x-2)^3

Answer 1

(a+b)^3 - (a-b)^3 =2b(3a^2-b^2)

so a=x b=2

2*2(3*x^2-2^2)
4(3x^2-4)

Answer 2

Answer:

$4(3x^2+4)$

Step-by-step explanation:

Given :$(x+2)^3-(x-2)^3$

To Find : Factorize

Solution:

$(x+2)^3-(x-2)^3$

Identity: $a^3-b^3=(a-b)(a^2+ab+b^2)$

a = x+2

b = x-2

Substitute in the identity

$(x+2-x+2)((x+2)^2+(x+2)(x-2)+(x-2)^2)$

$4(x^2+4+2x+x^2-4+x^2+4-2x)$

$4(3x^2+4)$

So, :$(x+2)^3-(x-2)^3$ = $4(3x^2+4)$