Answer:
(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).
Step-by-step explanation:
(a² - b²)(c² - d²) - 4abcd = a²c² - a²d² - b²c² + b²d² - 2abcd - 2abcd
=a²c² + b²d² - 2abcd - ( a²d² + b²c² + 2abcd ) = (ac-bd)² - (ad+ bc)²
[using the formula p² - q² = (p-q)(p+q) ]
= (ac-bd - ad - bc) (ac -bd + ad +bc)
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Verified answer
Answer:
(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).
Step-by-step explanation:
(a² - b²)(c² - d²) - 4abcd = a²c² - a²d² - b²c² + b²d² - 2abcd - 2abcd
=a²c² + b²d² - 2abcd - ( a²d² + b²c² + 2abcd ) = (ac-bd)² - (ad+ bc)²
[using the formula p² - q² = (p-q)(p+q) ]
= (ac-bd - ad - bc) (ac -bd + ad +bc)