Question

How do you factor `a^2-b^2+6b-9`?

Answer 1

`a^2-b^2+6b-9 = (a-b+3)(a+b-3)`

Explanation:

The difference of squares identity can be written:

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

We can use this with `A=a` and `B=b-3` as follows:

`a^2-b^2+6b-9 = a^2-(b^2-6b+9)`

`color(white)(a^2-b^2+6b-9) = a^2-(b-3)^2`

`color(white)(a^2-b^2+6b-9) = (a-(b-3))(a+(b-3))`

`color(white)(a^2-b^2+6b-9) = (a-b+3)(a+b-3)`