Question

Factorise (a^2-1) (b^2-1) +4ab​

Answer 1

SOLUTION

TO FACTORISE

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

CALCULATION

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

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

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

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

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

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