Question
Solve:$9 a^2-24 a^2 b^2+16 b^4-256$
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Answer
$9 a^2-24 a^2 b^2+16 b^4-256=\left(9 a^4-24 a^2 b^2+16 b^4\right)-256$
$=\left[\left(3 a^2\right)^2-2 \times 3 a^2 \times 4 b^2+\left(4 b^2\right)^2\right]-16^2$
$=\left(3 a^2-40^2\right)^2-16^2$
$=\left[\left(3 a^2-4 b^2\right)-16\right]\left[\left(3 a^2-4^2\right)+16\right]$
$=\left(3 a^2-4 b-16\right)\left(3 a^2-4 b^2+16\right)$
$=\left[\left(3 a^2\right)^2-2 \times 3 a^2 \times 4 b^2+\left(4 b^2\right)^2\right]-16^2$
$=\left(3 a^2-40^2\right)^2-16^2$
$=\left[\left(3 a^2-4 b^2\right)-16\right]\left[\left(3 a^2-4^2\right)+16\right]$
$=\left(3 a^2-4 b-16\right)\left(3 a^2-4 b^2+16\right)$
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