Factoring is too Tough: 2m^2 + 10m - 2n^2 + 10n

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Factoring is too Tough: 2m^2 + 10m - 2n^2 + 10n

Hey all! I love this website! It is the most comprehensive math website I have yet to find and it is great how each step is broken down into mini-steps. I spent hours yesterday studying from the site and I think it helped a lot...

Or, at least I WANT to think that it helped a lot. I think I read EVERYTHING on the site about factoring (and made detailed notes) but my math hw keeps confusing me.
Someone know how to factor:

2m^2 + 10m - 2n^2 + 10n

I get especially confused when I see four terms...

anyone?

hope everyone has/had a good day off!
butterflypoo3

Posts: 4
Joined: Tue Apr 14, 2009 12:16 am

butterflypoo3 wrote:Someone know how to factor:

2m^2 + 10m - 2n^2 + 10n

I get especially confused when I see four terms...

Always first look for any common factors that you can take out front. In this case, a "2" comes out of everything:

. . . . .$2\left[m^2\, +\, 5m\, -\, n^2\, +\, 5n\right]$

Now you have four terms, and no common factors. When this happens, it's usually a good idea to look for pairs of terms you can factor. To learn about this, try this page on factoring "in pairs". Once you've read that, the following should be useful:

. . . . .$2[m^2\, -\,n^2\,+\, 5m\, +\, 5n]$

The first pair is a difference of squares:

. . . . .$2[(m\, -\, n)(m\, +\,n)\, +\, 5m\, +\, 5n]$

From the second pair, you can factor out a "5":

. . . . .$2[(m\, -\, n)(m\, +\, n)\, +\, 5(m\, +\, n)$

There is now a common factor you can take out front, and then simplify the (m - n) + 5 that remains (by removing the parentheses).

stapel_eliz

Posts: 1758
Joined: Mon Dec 08, 2008 4:22 pm

Re: Factoring is too Tough: 2m^2 + 10m - 2n^2 + 10n

Ohhh, ok I get it now!
Thank you so much!

I knew how to do everything except the last step, it didn't occur to me to take (m-n) + 5 and make it (m-n+5).

Can I do that because I have two copies of (m+n)?
butterflypoo3

Posts: 4
Joined: Tue Apr 14, 2009 12:16 am

butterflypoo3 wrote:Can I do that because I have two copies of (m+n)?

Exactly!

stapel_eliz

Posts: 1758
Joined: Mon Dec 08, 2008 4:22 pm

Re: Factoring is too Tough: 2m^2 + 10m - 2n^2 + 10n

thx so much!
butterflypoo3

Posts: 4
Joined: Tue Apr 14, 2009 12:16 am