Question

Factorize each of the following expressions:

$a^4-16b^4$

Answer 1

Given: $a^4-16b^4$

$\therefore a^4-16b^4$
$=(a^2{)}^2-(4b^2{)}^2$
$=(a^2-4b^2)(a^2+4b^2)[\because a^2-b^2=(a+b\left)\right(a-b\left)\right]$
$=[a^2-(2b{)}^2\left]\right(a^2+4b^2)$
$=(a+2b)(a-2b)(a^2+4b^2)$

Hence, $a^4-16b^4=(a-2b)(a+2b)(a^2+4b^2)$.