Question

(a2-1)(b2-1)+4ab factorise this question

Answer 1

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

Step by step solution:

$({a}^{2} - 1)( {b}^{2} - 1) + 4ab \\ \\ {a}^{2} {b}^{2} - {a}^{2} - {b}^{2} + 1 + 4ab \\ \\ - ( {a}^{2} + {b}^{2} - 2ab) + 1 + {a}^{2} {b}^{2} + 2ab \\ \\ - ( {a - b)}^{2} + {(1)}^{2} + ( {ab)}^{2} + 2(1)(ab) \\ \\ - ( {a - b)}^{2} + ( {1 + ab)}^{2} \\ \\ ( {1 + ab)}^{2}- ( {a - b)}^{2} \\ \\ apply \: identity \\ \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ \\ (1 + ab - a + b)(1 + ab + a - b)$
Hope it helps you.

Answer 2

Step-by-step explanation:

Hope it helps

Thank you .