Question

Factorize the following using the Identities:
$m^8-n^8$

Answer 1

$m^8-n^8=(m^4{)}^2-(n^4{)}^2$
$=(m^4+n^4)(m^4-n^4)$ ------ [Using the Identity $a^2-b^2=(a+b)(a-b)]$
$=(m^4+n^4)\left[\right(m^2{)}^2-\left(n^2{)}^2\right]$$
$=(m^4+n^4)\left[\right(m^2+n^2\left)\right(m^2-n^2\left)\right]$ -----$[\because m^2-n^2=(m+n\left)\right(m-n\left)\right]$
$=(m^4+n^4)(m^2+n^2)\left[\right(m+n\left)\right(m-n\left)\right]$
$m^8-n^8=(m^4+n^4)(m^2+n^2)(m+n)(m-n)$