In Exercises 83–94, find each product.(x + y + 3)(x + y − 3)

Question

Accepted Answer

Hello, today we're gonna be performing multiplication on the given expression. So what we are given is M plus N plus five times the quantity M plus N minus five. Now, we can go ahead and simplify this by using the difference of squares and the difference of squares states that if you have a binomial in the form of A squared minus B squared, then this can be factored to give you the quantities A plus B times A minus B. Now you may be wondering how can we apply this property to the given expression? Well, notice that in both of the quantities we have the terms N plus N. So if we group up those terms together in the original expression that shows us that the expression matches the right hand side of the difference of squares. And here we can go ahead and allow our, a term to equal to M plus N and we can allow our B term to equal to five. So if we plug in these terms in the form of the factor binomial, we can rewrite the expression as M plus N squared minus five squared. Now, on the left hand, side, we can go ahead and rewrite N plus N as M plus N times the quantity M plus N. And in order to simplify this, we can go ahead and foil the quantities together M times M is going to give us M squared M times N is going to give us M N N times M is also going to give us M N. And finally, N times N is going to give us N squared. Now, we can combine the two like terms together, which in this case are both of the M N S. And that is going to give us M squared plus two M N plus N squared. And that's going to be the simplified form of M plus N squared. And on the right hand side, five squared is the same thing as five times five. And that is going to give us 25. So we can simplify this expression to give us M squared plus two M N plus N squared minus 25. And since we can't combine any more terms together, this is going to be the simplified form of the original expression. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And we'll go ahead and see you all in the next video.

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In Exercises 83–94, find each product.(x + y + 3)(x + y − 3)

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