Question

How do you factor by grouping `b^2 - 8b + 16 - c^2`?

Answer 1

`b^2-8b+16-c^2`
`= (b^2-8b+16)-c^2`
`= (b-4)^2 - c^2`
`= ((b-4)+c)((b-4)-c)`
`= (b+c-4)(b-c-4)`

The factoring of `(b-4)^2 - c^2` as `((b-4)+c)((b-4)-c)` is an instance of the identity:

`m^2-n^2=(m+n)(m-n)`

with `m=b-4` and `n=c`.