How do you factor the expression $(a^2-1)b^2-9(a^2-1)$ ?

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Answer 1 · 2016-01-11T04:38:59

Use the difference of squares identity to find:

$(a^2-1)b^2-9(a^2-1)=(a-1)(a+1)(b-3)(b+3)$

Use the difference of squares identity, which can be written:

$A^2-B^2=(A-B)(A+B)$

So:

$(a^2-1)b^2-9(a^2-1)$

$=(a^2-1)(b^2-9)$

$=(a^2-1^2)(b^2-3^2)$

$=(a-1)(a+1)(b-3)(b+3)$

How do you factor the expression (a^2-1)b^2-9(a^2-1)(a^2-1)b^2-9(a^2-1)?