a^4-16 b^4 =a^4-2^4 b^4 = (a^2 )^2- (2^2 b^2 )^2 = (a^2-2^2 b^2 ) (a^2+2^2 b^2 ) = [a^2-(2 b)^2 ] (a^2+4 b^2 ) (a-2 b)(a+2 b) (a^2+4 b^2 )

Solve: a^4-16 b^4

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

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Answer

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

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