Mathematics
Factorize:
(a2 - b2)(c2 - d2) - 4abcd
Factorisation
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Answer
Given,
⇒ (a2 - b2)(c2 - d2) - 4abcd
⇒ a2c2 - a2d2 - b2c2 + b2d2 - 4abcd
⇒ a2c2 + b2d2 - 2abcd - b2c2 - a2d2 - 2abcd
⇒ (a2c2 + b2d2 - 2 × ac × bd) - (a2d2 + b2c2 + 2 × ad × bc)
⇒ (ac - bd)2 - (ad + bc)2
⇒ [(ac - bd) + (ad + bc)][(ac - bd) - (ad + bc)]
⇒ (ac - bd + ad + bc)(ac - bd - ad - bc).
Hence, (a2 - b2)(c2 - d2) - 4abcd = (ac - bd + ad + bc)(ac - bd - ad - bc).
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