Question

Factorise:
(a^2-1)(b2-1)+4ab

Answer 1

(a^2-1)(b^2-1)+4ab
= a^2 b^2 - a^2 - b^2 +1+ 4ab

Now break 4ab into 2ab+2ab

= a^2 b^2 - a^2 - b^2 +1+ 2ab+2ab

Now arrange

= (a^2 b^2+ 2ab +1) - (a^2 - 2ab+ b^2)

=(ab +1)^2 - (a-b)^2

Using Formula x^2 -y^2 = (x-y)(x+y)

=[(ab+1) + (a-b)] [(ab+1) - (a-b)]

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

Answer 2

Answer:

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