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Factorisation by Regrouping Terms

Factorise : a...

Question

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

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Solution

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

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