In Exercises 67–82, find each product. (9x+7y)^2

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Hello. Today we're going to be determining the product of a given algebraic expression. So the algebraic expression given to us is five X plus two Y. That quantity squared. So in order to simplify this, we're gonna need to expand this entire quantity. Well five X plus two Y raised to the power of two means that you have two instances of at five X plus two Y being multiplied by each other. So this quantity could be rewritten as five X plus two Y times five X plus two Y. And in order to expand these, I'm going to need to foil them together. Foiling means that we take our first term five X. And multiply to the 1st and 2nd term of our second quantity and we take the second term to Y and multiply to the 1st and 2nd term of the second quantity. So doing that five X times five X is going to give me 25 X squared five X times two Y. Is going to give me 10 X Y. Two Y times five X. Is going to give me 10 X Y. And two Y times two Y. Is gonna give me four Y squared. All right. Now, in order to simplify this, I'm going to need to combine the like terms. While the only combine like terms here is 10 X. Y and 10 X. Y. Because they both have an xy term combining those together is going to give me the china meal 25 X squared plus 20 X Y plus four Y squared. And one more thing that I'm gonna do is go ahead and rewrite this. Try no meal in terms of power and doing that, is going to give me 25 X squared plus four Y squared plus 20 X Y. And that's gonna be the simplified version of this algebraic expression. And that means that the answer to this problem is going to be D. So I hope this video helps you in understanding how to simplify an algebraic expression and I'll go ahead and see you all in the next video.

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