# Thread: (Algebra I) - help with polynomial

1. ## (Algebra I) - help with polynomial

Hello all,

I've received so much help in this forum and really appreciate that you guys are able to figure out what I'm really asking despite my typos.

Anyway, here's another one from Beginning Algebra (sixth ed.); Chapter 5, Section 5.2 Adding and Subtracting Polynomials.
85. (11r2s + 16rs - 3 - 2r2s2) - (3sr2 + 5 - 9r2s2)

The answer is: 8r2s + 16rs - 8 + 7r2s2
I got the same answer except for 8r2s. I don't understand how 8r2s is a solution because r2s is not in the subtrahend. My understanding of operations on Polynomials is that the variables and exponents should be in the same order. But in this case, are r2s and sr2 the same?

Also, where can I find more information on the order that the result should be simplified to?

Thank you.

2. ## Re: (Algebra I) - help with polynomial

multiplication of real numbers commutes so $r^2 s = s r^2$

3. ## Re: (Algebra I) - help with polynomial

Originally Posted by romsek
multiplication of real numbers commutes so $r^2 s = s r^2$
Ok... *sigh* So really what I should be looking for when combining like terms is; in this case, r2. The s can be anywhere because as you stated, it commutes: the result is the same.

4. ## Re: (Algebra I) - help with polynomial

Originally Posted by alexcordero
Ok... *sigh* So really what I should be looking for when combining like terms is; in this case, r2. The s can be anywhere because as you stated, it commutes: the result is the same.
you have to match up both the variables and the exponents

you can combine, for example $s r^2 + r^2 s = 2 r^2 s$

or $s^2 r^2 + r^2 s^2 = 2 r^2 s^2$

but you can't combine, for example $r^2 s + s^2 r$

5. ## Re: (Algebra I) - help with polynomial

Yep! I just looked at the rest of the problem using what you initially showed me and I get it now. Initially I was confused because I thought that if r2 is going to be used, then why not use r2s2? But! r2s2 is not the same as r2s or sr2, with respect to r2. Again, thank you!!