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प्रश्न
Factorise the following:
(a2 - b2)(c2 - d2) - 4abcd
उत्तर
(a2 - b2)(c2 - d2) - 4abcd
= a2c2 - a2d2 - b2c2 + b2d2 - 4abcd
= a2c2 + b2d2 - 2abcd - a2d2 - b2c2 - 2abcd
= (a2c2 + b2d2 - 2abcd) - (a2d2 + b2c2 + 2abcd)
= (ac - bd)2 - (ad + bc)2
= [(ac - bd) + (ad + bc)][(ac - bd) - (ad + bc)]
= (ac - bd + ad + bc)(ac - bd - ad - bc).
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