Question

How do you factor by grouping `m^2-n^2+5m-5n`?

Answer 1

`(m+n+5)(m-n)`

Explanation:

Group as `(color(red)(m^2-n^2))+(color(blue)(5m-5n))`

Recognize `(color(red)(m^2-n^2))` as the difference of squares which can be factored as `color(red)((m+n)(m-n))`

Extract the common factor of `color(blue)5` from `(color(blue)(5m-5n))` to get `color(blue)(5(m-n))`

Now we have
`(color(red)(m^2-n^2))+(color(blue)(5m-5n))=color(red)((m+n)(m-n))+color(blue)(5(m-n))`

Extracting the common factor of `(m-n)` from these two terms gives
`color(white)("XXX")(color(red)(m+n)+color(blue)5)(m-n)`