Question:
Factorize each of the following algebraic expression:
9a4 − 24a2b2 + 16b4 − 256
Solution:
$9 a^{4}-24 a^{2} b^{2}+16 b^{4}-256$
$=\left(9 a^{4}-24 a^{2} b^{2}+16 b^{4}\right)-256$
$=\left[\left(3 a^{2}\right)^{2}-2 \times 3 a^{2} \times 4 b^{2}+\left(4 b^{2}\right)^{2}\right]-16^{2}$
$=\left(3 a^{2}-4 b^{2}\right)^{2}-16^{2}$
$=\left[\left(3 a^{2}-4 b^{2}\right)-16\right]\left[\left(3 a^{2}-4 b^{2}\right)+16\right]$
$=\left(3 a^{2}-4 b^{2}-16\right)\left(3 a^{2}-4 b^{2}+16\right)$
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