In Exercises 59–66, perform the indicated operations. Indicate th...

Question

In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^4 y^2−5x^2 y^2+3xy)+(−18x^4 y^2−6x^2 y^2−xy)

Accepted Answer

Hello today we're going to be simplifying an algebraic expression. So the expression given to us is X to the eighth, Y squared z minus X squared y squared z squared plus two X Y Z plus four X to the eighth, Y squared z minus x squared y squared z squared minus two X y Z. Okay. So in order to simplify this, we're going to need to first open up these pairs of parentheses. But if you notice these quantities are just being added together. So if you just distribute this positive sign into this trin Amiel, it's not going to change any of the signs of the given terms. So we can just go ahead and rewrite this entire expression without the parentheses. So doing that, we're going to get X to the eighth, Y squared z minus x squared y squared z squared plus two X Y Z. And that's been added by four X to the eighth, Y squared z minus x squared y squared z squared minus two X Y Z. All right. Now, in order to simplify this, all we need to do is just go ahead and add the like terms together. Well, the first combine double pair of like terms is positive two, X, Y Z and negative two X Y. Z. Since one is positive two. And the other's negative to these are just going to cancel each other out. And the other pair of combine herbal terms we have is four X to the eighth, Y squared Z and X to the eighth Y squared Z. This is the same thing as saying four of this quantity plus one of this quantity. So four plus one is going to be five and what we are left with is five X to the eighth, Y squared Z. And the final combine double pair of like terms is going to be negative X squared y squared Z and negative X squared y squared Z. This is like saying negative one minus one of each quantity. And that's going to give us negative two, X squared y squared Z squared. And that's going to be the simplified version of this algebraic expression. And that also means that the solution to this problem is going to be deep. So I hope this video helps you in understanding how to simplify this algebraic expression and I'll go ahead and see you all in the next video.

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