Factor each trinomial, if possible. See Examples 3 and 4. 32a^2+4...

Question

Factor each trinomial, if possible. See Examples 3 and 4. 32a^2+48ab+18b^2

Accepted Answer

Welcome back. I am so glad you're here. We are given this polynomial 75 A squared plus 180 A B plus 108 B squared. And we're asked to factor this polynomial. Well, the first thing we want to do is look at all three of these terms and see if they have anything in common that can be factored out. And well, the first terms got an A squared. The second term has an A B and the third term has A B squared. They don't all share a common variable, but looking at 75 181 all three of those might share a factor in common. So looking at all three of them, they're all three divisible by three. So we can factor a three out in front and then what will be left over? And we will do this division here. 75 divided by three is 25. So that's 25 a squared. And then 180 divided by three is 60. So that's plus 60. Bring down the A and the B And then 108 divided by three, that is 36. So plus 36 b squared. And now we take a look at what's left here in the parentheses and see if we can factor it any further. There's nothing else that we can bring out in front. However, looking at these, this 25 A squared. Well, first, we would ask ourselves what times what equals 25 A squared. But notice there are quite a few squares, there are 25 is five squared And a squared is a squared. We could also write this parentheses, five a squared. And then after we figure out what times what gives us the first one, we would look at the third one and say what times what gives us that? Well, what times what gives us 36 B squared? That's also a lot of squares, 36 is six squared and B squared is B squared. And we could also write this parentheses six B squared. And this just might fulfill the condition where sometimes we have X squared plus two X Y plus Y squared. And if that's the case that is equal to this fully factored X plus Y and parentheses squared. So let's see if we've got this plus two XY in the middle. So what's our X Here? Our X is the first thing being squared. So X is equal to 58. What's our, why are, why is the second thing being or the end thing? The last thing being squared. So why equals six b? And for two X Y, we're going to take two times X which is five A times Y, which is six B, two times five times six. That equals 60. Bring down our A and R B 60 A B. Yes, that does match what we've got up here. And we do have X squared plus two XY plus Y squared. So now we can set that equal to parentheses X plus Y squared. So our X again is five A plus R Y is six B. Now, very important that we don't forget this. We factored a three out at the beginning and we have to include that as part of our factoring. So our final answer is three times five A plus six B in parentheses squared. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

Factor each trinomial, if possible. See Examples 3 and 4. 32a^2+48ab+18b^2

Key Concepts

Factoring Trinomials

Greatest Common Factor (GCF)

Quadratic Formula

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