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

(a c - b d + a d + b c) (a c - b d - a d - b c)

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(a c + b d + a d + b c) (a c - b d - a d - b c)

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(a c - b d + a d + b c) (a c + b d - a d - b c)

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(a c - b d + a d - b c) (a c - b d - a d - b c)

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Solution

The correct option is A $(a c - b d + a d + b c) (a c - b d - a d - b c)$
$(a^{2} - b^{2}) (c^{2} - d^{2}) - 4 a b c d$
$= a^{2} c^{2} - a^{2} d^{2} - b^{2} c^{2} + b^{2} d^{2} - 2 a b c d - 2 a b c d$
$= (a c)^{2} - 2 (a c) (b d) + (b d)^{2} - ((a d)^{2} + 2 (a d) (b c) + (b c)^{2})$
$= (a c - b d)^{2} - (a d + b c)^{2}$
$= (a c - b d + a d + b c) (a c - b d - a d - b c)$

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Similar questions

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

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