Factorize: $(a^{2} + b^{2} - c^{2})^{2} - 4 a^{2} b^{2}$

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Solution

We have,
$(a^{2} + b^{2} - c^{2})^{2} - 4 a^{2} b^{2}$
$\Rightarrow (a^{2} + b^{2} - c^{2})^{2} - (2 a b)^{2}$
$\Rightarrow (a^{2} + b^{2} - c^{2} + 2 a b) (a^{2} + b^{2} - c^{2} - 2 a b)$

Hence, this is the answer.

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