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3 UB example of two 1 77 pue 7 such that 7 x 71...

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3 UB example of two 1 77 pue 7 such that 7 x 71

3 UB example of two 1 77 pue 7 such that 7 x 7 1



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Multiply. See Example 7. $$ \left(\frac{1}{3} a^{2}-7\right)\left(\frac{1}{3} a^{2}+7\right) $$

We want to find three X minus seven. Why all squared? This is a special product, and we know this is going to equal first term square. Keep the same signs that will be a minus Now, the two times the first term times the second term and then plus the second term squared. So our answer is going to be nine x squared minus 42 x y plus 49 y squared.

We want to find to a minus three, all squared. So this is a special product. When we square a binomial, we know that's going to equal to the first term squared. We keep the same sign, so that would be a minus. And there will be two times the first term on the second term. And then plus, the second terms were so this ends up being for a squared minus 12 a last nine.

We want to find three times X minus two squared. Okay. So we can see that we have X minus two squared, which is a special product, and that is going to equal to, um, the first term cleared. And we keep the same sign, so that'll be minus. It'll be two times the first term times the second term and then plus a second channel script. Okay, so don't forget that we still have the three in the front, so we'll leave. We'll need to write down three. And that's three times that. So this is going to equal to three times. That'll be X squared minus four X plus four. And then we just have to distribute the three now, so that'll be three X squared, minus 12 x plus.

I'm going to show you a couple of ways to simplify this expression, so the fast way is if you recognize that two X minus seven and seven minus two X are opposites, and when you divide opposites, you get negative one. Boom. There's your answer. Negative one, However, if you want to show it with more steps, what you can do is you can rewrite your denominator as negative two X plus seven. I've just rearranged the two terms on the bottom. Then you can factor a negative out of both terms of your denominator so fi factor out a negative. I have negative one times the quantity to X minus seven, and then you realize that you have a common factor of two X minus seven on the top and bottom that you can remove and all that leaves you with is the negative. So that means you have negative one


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