Thread: Reverse FOIL Factoring

My question is what to do if there is a random variable in the middle number/variable in a trinomial when factoring the trinomial using reverse FOIL. The problem itself was n^2-26mn+25n^2. When I factored it using the outer numbers/variables, I ended up getting (n-25n)(n-n), and when I redistribute everything, it becomes n2-26n^2+25n^2, and the middle number/variable should be -26mn. How do I get the m and get rid of the extra n?

Originally Posted by Vinefeather

My question is what to do if there is a random variable in the middle number/variable in a trinomial when factoring the trinomial using reverse FOIL. The problem itself was n^2-26mn+25n^2. When I factored it using the outer numbers/variables, I ended up getting (n-25n)(n-n), and when I redistribute everything, it becomes n2-26n^2+25n^2, and the middle number/variable should be -26mn. How do I get the m and get rid of the extra n?

Assuming there is no typo in n^2-26mn+25n^2, just combine terms and factor out an n. We have

n^2-26mn+25n^2

-26mn+26n^2

26n(-m+n)

Thank you sooooo much!!~ <3 Can't believe I didn't think of that sooner, lol.

Another question, how would I solve this: 5r^2+29rt-5t^2? I can't seem to get the 29rt no matter how hard I try... D:

Originally Posted by Vinefeather

Another question, how would I solve this: 5r^2+29rt-5t^2? I can't seem to get the 29rt no matter how hard I try... D:

This expression does not factor nicely, as far as I can tell. Possibly your teacher/book just intends you to leave it as it is.

I'm curious to know if there is a nice solution here, please report back if nobody answers and if you get such an answer from your teacher/book. I might just be blind.

(Edited)