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Multiplying Polynomials: Special Cases - Problem 1 4,514 views
Here I’m given a binomial that’s squared. That tells me already that my answer is going to be what we call a perfect square trinomial.
One thing I want to make sure I point out before I do this problem is I mean for that to be 2 times b, not 26. I just make to sure that is clear before I do the problem. I’m not doing 26 there, it’s 2 times a letter b. My hand writing is kind of tricky on that one.
Another thing I want to make sure you guys are clear on is what this means. This means the quantity 3a plus 2b times itself 3a plus 2b again. So when I go through to do this problem, I’m going to be using FOIL. I’m going to be Foiling this guy times itself. FOIL remember stands for first, outers, inners, last. The product of my first is going to be 9a². Product of my outers 3a times 2b is going to be 6ab, product of my inners is going to be 6.
I’m going to write this as ab in that same order. Here is what I mean, a lot of times students would see this and they would write 6ba, but because of the properties of multiplication, 6ba is actually the same thing as 6ab, so my outers and inners actually are exactly the same, tricky. Outers and inners, now I need to do last. 2b×2b is going to be 4b². The last thing I need to do is finish my Foiling process is combine these inside terms. So I’ll have 9a² plus 12ab plus 4b².
That’s my final answer; again it’s called a perfect square trinomial because it was the result of squaring a binomial. This is what we call a special case or a special product, because it has the form a² plus 2ab plus b², but check it out these aren’t, it’s not just plain old a² and b², it’s like an extra constant that goes in there that comes out of these guys. The 3 got squared, the 4 got squared and then here I have 2 times the product of 3, 2.
So this is again a special product. You don’t have to necessarily remember the fancy name for it, the Perfect Square trinomial, but you do have to be able to do this Foiling process correctly if all you’re given is this original statement.