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

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

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

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

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

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Solution

The correct option is C $(a c - b d) (b c - a d)$
Given, ${(d}^{2} + c^{2}) a b - {a^{2} c d - b}^{2} c d,$

$= a b d^{2} + a b c^{2} - c d a^{2} - c d b^{2},$
rearrange and,
$= b c (a c - b d) - a d (a c - b d)$

$= (a c - b d) (b c - a d)$

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