Factorize the equation $(a^{2} - 1) (b^{2} - 1) + 4 a b$

(a^{2} - 1) (b^{2} - 1) + 4 a b = (a b + 1 + a - b) (a b - b)

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(a^{2} - 1) (b^{2} - 1) + 4 a b = (a b + 1 - a - b) (a b + 1 - a + b)

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(a^{2} - 1) (b^{2} - 1) + 4 a b = (a b + 1 + a - b) (a b + 1)

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(a^{3} - 1) (b^{2} - 1) + 4 a b = (a b + 1 + a - b) (a b + 1 - a - b)

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Solution

The correct option is B $(a^{2} - 1) (b^{2} - 1) + 4 a b = (a b + 1 - a - b) (a b + 1 - a + b)$
$(a^{2} - 1) (b^{2} - 1) + 4 a b$
$= a^{2} b^{2} - a^{2} - b^{2} + 1 + 4 a b$ $= a^{2} b^{2} + 2 a b + 1 - (a^{2} + b^{2} - 2 a b)$
$= (a b + 1)^{2} - (a - b)^{2}$
$= (a b + 1 + a - b) (a b + 1 - a + b)$

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