Factor each trinomial, if possible. See Examples 3 and 4. 9m^2n^2...

Question

Factor each trinomial, if possible. See Examples 3 and 4. 9m^2n^2+12mn+4

Accepted Answer

Welcome back. I am so glad you're here. We have this polynomial 81 A squared, B squared plus 198 A B plus 121 and were asked to factor it. Normally, when we start factoring, we take a look at the first term and we say, well, what two things go into this? But we notice looking at this, we have a lot of squares here. 81 that's nine squared A squared is A squared and B squared is B squared. We could rewrite this, we could put in parentheses nine times A times B and then square that whole thing. So that's a lot of squares. Very interesting. Next, typically we'd look at this last term and we'd say, well, what times what goes into this? And well, that's another square 121 is 11 squared. So it's possible that we have a special situation here when we have X squared plus two X Y plus Y squared, that will be equal to parentheses X plus Y squared. And this is the factor. So let's see if we do in fact have this situation. So X squared here while our X Would be nine AB, why squared the why would be and so for two times X times Y we're going to take two times. What's X X is nine A B Times? Why? Why is 11? Alright. Well, if we take two times nine times 11, that is 198 and bring down our times eight and times B and look that does match, we do have plus two X Y in the middle. So this does meet this condition. So I'll bring down plus 198 A B. This does meet this special situation so we can set this equal to X plus Y squared. So what's R X R X is nine A B? What's Ry, ry is 11 and squared? And that is factored. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Factor each trinomial, if possible. See Examples 3 and 4. 9m^2n^2+12mn+4

Key Concepts

Factoring Trinomials

Greatest Common Factor (GCF)

Perfect Square Trinomials

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