Question

Factorise: a2b 2 -a 2 -b 2+1.

Answer 1

Step-by-step explanation:

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

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