Resolve in to factors $x^{4} + 16 x^{2} + 256$ .

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Solution

Taking $a = x$ and $b = 4$ we have
$x^{4} + 16 x^{2} + 256 = a^{4} + a^{2} b^{2} + b^{4} = (a^{2} + a b + b^{2}) (a^{2} - a b + b^{2})$
Substituting back $a = x$ and $b = 4$ we obtain
$x^{4} + 16 x^{2} + 256 = (x^{2} - 4 x + 16) (x^{2} + 4 x + 16)$

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