Question

Factorize

​$m^4-256$ [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

$m^4-256=(m^2{)}^2-{16}^2$

$(m^2-16)(m^2+16)$

Now, $(m^2+16)$ cannot be factorised further, but $(m^2-16)$ is factorisable again.

$m^2-16=m^2-4^2$

$=(m–4)(m+4)$

Therefore, $m^4-256=(m–4)(m+4)(m^2+16)$