factorize:(1 - a^2) (1 - b^2) + 4ab
Mathematics · High School · Thu Feb 04 2021
llm
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We have, (1 - a²) (1 - b²) + 4ab = 1- b² - a² + a²b² + 4ab
Split the 4ab into 2ab and 2ab
=1-b²-a²+a²b²+2ab+2ab
=(a²b² + 2ab + 1) -(a²+2ab+b²)
= (ab+1)² - (a+b)²
By (x+y)² = x²+2xy+y²
and, (x-y)²= x²-2xy+y²
=(ab+1-a+b){ab+1+a-b)