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

Jan 11, 2016

Use the difference of squares identity to find:

$\left({a}^{2} - 1\right) {b}^{2} - 9 \left({a}^{2} - 1\right) = \left(a - 1\right) \left(a + 1\right) \left(b - 3\right) \left(b + 3\right)$

#### Explanation:

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

${A}^{2} - {B}^{2} = \left(A - B\right) \left(A + B\right)$

So:

$\left({a}^{2} - 1\right) {b}^{2} - 9 \left({a}^{2} - 1\right)$

$= \left({a}^{2} - 1\right) \left({b}^{2} - 9\right)$

$= \left({a}^{2} - {1}^{2}\right) \left({b}^{2} - {3}^{2}\right)$

$= \left(a - 1\right) \left(a + 1\right) \left(b - 3\right) \left(b + 3\right)$