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

1 Answer
Jun 18, 2018

(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)