Question

Factorize the following

4b2c2 - (b2 + c2 - a2 )2

Answer 1

Solution :

4b²c² - (b²+c²-a²)²

= (2bc)² - (b²+c²-a²)²

=(2bc+b²+c²-a²)(2bc-b²-c²+a²)

=[(b²+c²+2bc)-a²][a²-(b²+c²-2bc)]

= [(b+c)² - a²][a²-(b-c)²]

= [(b+c+a)(b+c-a)][(a+b-c)(a-b+c)]

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