Question

Using identities , factorise the following (x-2)^4 - x^4​

Answer 1

Given:

• Factorise (x - 2)^4 - x^4

Solution:

$\implies (x - 2)^4 - x^4$

$\implies [(x-2)^2] \times [(x-2)^2] - x^4$

$\implies [x^2 - 4x + 4] \times [x^2 -4x + 4] - x^4$

$\implies [x^2 (x^2 - 4x + 4)] -$$[4x (x^2 - 4x + 4)] + [4(x^2 - 4x + 4)] - x^4$

$\implies [x^4 - 4x^3 + 4x^2] - [4x^3 +$$16x^2 - 16x] + [4x^2 - 16x + 16] - x^4$

$\implies \bf -8x^3 + 24x^2 - 32x + 16$