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Multiplying Larger Degree Polynomials using Distributing - Problem 2
Here I have a binomial, meaning 2 terms being multiplied by a trinomial which has 3 terms. I’m going to do this multiplication using distributing, but I have to do the distributing kind of twice. Here is what I mean.
This 3x has to get distributed onto each of these 3 terms and then this positive 2 gets distributed onto all 3 of those terms. I’m also going to show you a strategy that I like to use to write these problems vertically. Here is what I mean.
First thing I’m going to do is take this 3x and multiply it by each of the 3 terms in my trinomial. 3x times 4x² gives me 12x to the third. 3x times -2x is -6x² and then 3x times +10 is +30x. That tells me I’m done with that first term. Now I’m going to use a different color, you can if you want to, you don’t have to, and I’m going to do 2 times each of these 3 terms.
2 times 4x is 8x². I’m going to write that vertically under my other x² term. Here is what I mean. It’s going to help me later when it comes to combining my terms. 2 times 4x² done, 2 times -2x will be -4x, I’m writing it under my other x term and then 2 times 10 of course is 20. So here is why that writing vertically helps me. Now that I’m ready to write the answer, it’s kind of easy for me to combine like terms when I haven’t written vertically like this. I know my only x to the third term is that 12 right there -6x² plus 8x² gives me +2x²'s, adding vertically I’ll have 26xs and then plus 20.
So in order to do this problem, I did a couple of strategies that you may or may not want to try. One thing I did is I drew these little rainbow things to help remind myself that 3x gets multiplied by all of those. Another strategy I did was using color. I used purple to show my products that the 3x was creating and then I used red to show my products that came out of these 2, and then the last strategy I used that you might want to try is setting it up vertically like this and the reason why I liked that is because it made it really easy when it came time for me to combine like terms.
It’s totally up to you how you approach these problems. You don’t have to use any of those strategies I showed you, but you do have to be really careful to make sure that each of the terms of your binomial get multiplied by all three terms in the trinomial.