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Adding and Subtracting Polynomials - Problem 3

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Here I’m given this subtraction problem that involves two polynomials. I’m going to do this problem in 2 ways to show you guys a couple different approaches you might use. But before I start the problem, I noticed a couple of tricks to it.

First thing this is a trinomial with 3 terms, that’s only a binomial which means I’m going to have to do something tricky to be careful with my exponents. Also this is the subtraction sign, so I need to be really careful to keep straight in my head that that negative sign distributes to both of these terms.

So first I’m going to show you how you might write this out using distributing, distributing that minus sign. My first trinomial is going to stay the same. 29y² minus 3y, then I’m going to distribute this minus to both of these terms. -2y to the third minus 6, that’s the most common mistakes students make in these kinds of problems. They forget to distribute that negative sign.

Once I have it written out, I’m going to go through and combine like terms looking for all my y to thirds, I have 30 of them take away 2 of them that’s 28y to the thirds. Those guys are already done I’m going to cross them out. -29y², be careful don’t lose that negative sign, that’s another common mistake students make. Now that guy is done. Regular ys I have -3 and then my constant term is just -6, and I know I’m done now because everything has been crossed out, everything has been accounted for. This is my final answer.

That’s one way to approach this problem. Another way a student might approach this problem is by writing these guys vertically. So I’m going to erase this if you’re writing this down real quick here comes the erasing. Okay I’m guessing you’re done writing done. Okay. What I’m going to do is write these things vertically and show you how you might arrange it vertically in case that helps you. This is usually good for visual learners, if you’re a visual leaner like me.

I have this whole trinomial; I’m going to subtract 2y to the third plus 6. Writing vertically my 2y to the third term is going to go here under the other y to the thirds. So now I’m about to subtract vertically, and then I have take away 6, so that take away piece is going to have to go out here because my first polynomial didn’t have any constant or take away a positive number term.

Once I have it set up like this, I’m going to subtract vertically. 30 take away 2 is 28y to the third, -29 just stays the way it was because it doesn’t have any other term from the second polynomial that had a y squared piece take away 3y, and then just take away 6. This is the same answer I had before, but it might help you guys to see it vertically like this I think because when you first start doing addition and subtraction problems like in third and forth grade or whatever, a lot of times they’re written like this. So this just might help trigger your brain and remind you what to do.

Either way again you guys, you’ve got to be super careful with the negative signs. That’s the place where students make mistakes. Keep that negative attached to the 29, that’s not a positive 29, it’s a big deal, so be careful with that and you guys will get A pluses on these homework problems.

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