Perform the indicated operations. Indicate the degree of the resu...

Question

Perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^2-8xy+y^2)+(-8x^2-9xy-4y^2)

Accepted Answer

Welcome back. I'm so glad you're here. We are performing the indicated operation which is addition with these two polynomial. So adding them together. We can just rewrite them without the parentheses because there's no minus that's getting distributed to the second term or any things like that? No multiplication happening. So we can just write it two X squared minus four X y plus two Y squared plus three X squared plus nine X y minus three Y squared. And now we can just start off by combining like terms. So any x squares, we got two of them plus three more. So we've got five X squared. Um Do we have any more X wise, negative four of them? Plus nine of them? That's going to be plus five X. Y. And how about these y squares? We got two of them minus three of them, so minus y squared. That's as simplified as that's going to get. And now before we go searching through the answers we've also got to figure out the degree of the resulting polynomial. So to figure out the degree of the resulting polynomial, what we're going to do is look at the degree of each term. To look at the degree of each term, we see the exponents for all the variables. And this first term five X squared. It's only got that too. So the terms degree is too, for the second one here there's like invisible ones. Um for the exponents of the X and the Y. So one plus one is to the degree of that term is to this Y squared is just got the two. So that's degree is two. And now you look at the terms degrees and you say which of these is the highest. Well, they're all the same, but so it's just going to default to two. And now we look at our answer choices and that's going to give us answer choice. B. Well done. You've done it, we'll catch you on the next one.

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