Question

Factorize the following algebraic expression:

$9a^4-24a^2{b}^2+16b^4-256$

Answer 1

Given: $9a^4-24a^2{b}^2+16b^4-256$

$\therefore 9a^4-24a^2{b}^2+16b^4-256$

$=\left[\right(3a^2{)}^2-2\left(3a^2\right)\left(4b^2\right)+\left(4b^2{)}^2\right]-256$

Using the formula, $(x-y{)}^2=x^2-2xy+y^2$

$=(3a^2-4b^2{)}^2-256$

$=(3a^2-4b^2{)}^2-(16{)}^2$

Using, $x^2-y^2=(x+y)(x-y)$

$=(3a^2-4b^2+16)(3a^2-4b^2-16)$

$\therefore 9a^4-24a^2{b}^2+16b^4-256=(3a^2-4b^2+16)(3a^2-4b^2-16)$