Question

(a2-1)(b2-1)+4ab factories it​

Answer 1

Answer:  

$(ab+1 -(a+b)) (ab+1 +(a+b))$

Step-by-step explanation:

if we open this expression

$a^{2}b^{2} +1 -a^{2} - b^{2} +4ab$

If we re arrange this we get,

$a^{2} b^{2} +1 +2ab -(a^{2}+ b^{2} - 2ab )$  

therefore by using the identity

a² + b² ± 2ab =  (a ± b)²

we get

$(ab+1)^{2} - (a+b)^{2}$

and by using the identity

x² - y² = (x+y)² (x-y)²

we get

$(ab+1 -(a+b)) (ab+1 +(a+b))$

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