(a²-b²)(c²-d²)-4abcd

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Solution

(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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