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

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

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

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

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

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Solution

The correct option is C $(a^{2} + b^{2} - 4 c^{2} - 2 a b) (a^{2} + b^{2} - 4 c^{2} + 2 a b)$
$(a^{2} + b^{2} - 4 c^{2})^{2} - 4 a^{2} b^{2}$
= $(a^{2} + b^{2} - 4 c^{2})^{2} - (2 a b)^{2}$
$[∵ a^{2} - b^{2} = (a + b) (a - b)]$
= $(a^{2} + b^{2} - 4 c^{2} - 2 a b) (a^{2} + b^{2} - 4 c^{2} + 2 a b)$

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