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Multiplying Larger Degree Polynomials using Distributing - Problem 3
Here I have to multiply 2 trinomials. I’m going to show you a couple of strategies that I like to use when I’m doing these problems. One thing I’m going to use is use 3 different colors to represent each of the terms of my original trinomial, getting multiplied by my second trinomial. I’m also going to write things vertically so when it comes time to combine like terms, everything will be set up for me.
Now before I show you this problem, I want to tell you guys the most common mistake students make are these errors with negative signs like little careless errors. You’ll see that Math is not really that difficult. The trickiest part with these is keeping your stuff straight, and that’s why I like the strategies like color and writing vertically. Let me show you what I mean.
First thing I’m going to do is take this 2x² and multiply it by all three terms in my second trinomial, so I have to do 2x² times -3x², that gives me -6x to the fourth. 2x² times +2x is going to be 4x to the third, and then 2x² times positive, excuse me 2x² times -1 is -2x². Now I’m all done with that guy I don’t have to deal with him any more. I’m going to move on to the next term in that trinomial, the –x. And that –x needs to get multiplied again by all 3 of these terms in my second trinomial.
Here also I’m using a different color to help me keep track of where I’m getting all these numbers and I’m also going to write things vertically. Like –x times -3x² is +3x to the third. I’m going to line it up with this x to the third term, so later on when I’m combining like terms, it will just go more quickly. So that piece is done -x times +2x, careful with the negative sign, +x. Now I’m all done with that –x term.
The last thing I need to work with is that positive 6. Using a third color, I’m going to show how +6 gets multiplied by all 3 of these second trinomials. See how this is kind of tricky like keeping track of everything that’s getting multiplied by everything else, that’s where these errors happen, you’ve got to keep your stuff straight and that’s why the color helps me.6 times -3x² is going to be -18x² lining it up again so that my combining like terms step will be easier. 6 times 2x is 12x and then 6 ×-1.
The last thing I’m going to do I’m happy now that I have everything lined up vertically because combining like terms will be a snap. -6x to the fourth that’s my only x to the fourth term. I’m going to have 7x to the thirds, -22x²'s, 13x's and then take away 6 at the end. This whole big polynomial mean mess is my final answer and so assuming that I was really careful with all my negative signs, and assuming that everything got lined up correctly and all my exponents are correct I didn’t like make a mistake and accidentally write that 3 or should be 4 or whatever, this should be the correct answer.
One last thing before you guys try your homework, I want to remind you this Math is not difficult, it’s just the Distributive property. The difficult part is keeping all your stuff straight. If you try to write it vertically, that will really help you, and if you want to use color, that’s another thing that will help you. Also as a Math teacher when students use this method, it’s really easy for me to find their errors and give them help, so if your tutor, if you work with a tutor, or if you work with your Math teacher outside of class, this method will help them find your errors and help you learning how to do these problems correctly.