In Exercises 83–94, find each product.(5x + 7y − 2)(5x + 7y + 2)

Question

Accepted Answer

Hello, today we're going to be performing multiplication on the given expression. So what we are given is eight M plus 11 N minus six times the quantity eight M plus 11 N plus six. Now we're gonna go ahead and simplify this using the difference of squares and the difference of squares states that if we have a binomial in the form of A squared minus B squared, this can be factored to give us the form of A plus B Times A. -7. And in order to use this property, I'm gonna go ahead and quickly rewrite the given expression. Let's see what happens when I group up AM plus 11 M in both of the quantities. If I were to group up those two terms in both of the quantities, this expression matches the form of A plus B times A minus B. Here, we're going to let A equal to eight M plus 11 N and we're going to allow B to equal to six. So we can go ahead and rewrite the given expression to be AM plus 11 N squared minus six squared. Now, on the left hand side, in order to simplify eight M plus 11 N squared. We're going to have to foil the quantity together so we can rewrite the left hand side to give us eight M plus 11 N times the quantity eight M plus 11 N. Then in order to simplify this, we're going to foil it. So am times AM is going to give us 64 M squared eight M times 11 N is going to give us 88 M N 11 N times eight M is going to give us 88 M N and finally 11 N times 11 N is going to give us 121 N squared. And if we combine the like terms together 88 M plus M is going to give us 176 M N. So we can rewrite this as 64 M squared plus 176 M N plus 121 N squared. And on the right hand side, six squared is the same thing as six times six, which is going to give us 36. So we can rewrite this expression to give us 64 M squared plus 176 M N plus 121 N squared minus 36. And since we can't combine any quantities together, this is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be b so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 83–94, find each product.(5x + 7y − 2)(5x + 7y + 2)

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