In Exercises 69–82, multiply using the rule for the product of th...

Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms.

(8x + 7y)(8x − 7y)

Accepted Answer

Hey, everyone in this problem, we're asked to perform multiplication on the given expression. And the expression is two binomials multiplied together. So we have the first binomial two M plus 10 N multiplied by the second binomial two M minus N, we're given four answer choices. Option A four M squared minus 40 M N minus 100 N squared. Option B four M squared minus 100 N squared. Option C four M squared plus 40 M N minus 100 N squared. In option D four M squared plus N squared, we're gonna start by rewriting the expression we were given. So we have the binomial two M plus 10 N multiplied by the binomial two M minus 10 N. And notice here this is the expression for a difference of squares. Yeah. So we call a difference of squares. We have the expression A plus B, we have the binomial A plus B multiplied by the binomial A minus B. This can be written as the difference of squares A squared minus B squared. So the expression we were given is the left hand side of this equation. We have two M plus 10 N multiplied by two M minus 10 N. So we have the left-hand side with a equal to two M and B equal to 10 n. And this difference of squares expression gives us an easy way to expand that multiplication. We just get these two terms A squared minus B squared. So our expression two M plus 10 N multiplied by 2 M -10 N is equal to A squared where A is two M. So we have two M squared minus B squared, 10 and squirt. So now the multiplication part is done. OK, using the difference of squares equation formula, we've got the multiplication step done. And we're left with just simplifying this expression. Now we have two M all squared. OK. Be careful here. The square has to apply to the two as well as the M. So we get two squared is four and M squared is M squared. So we get four M squared, we have 10 N squared. OK. 10 squared is 100 N squared is N squared. So we have minus 100 N squared and that's the result of our multiplication. That's the simplified expression that we were looking for. Now, if you didn't recognize that this was a difference of squares, that's OK. We have two binomials multiplied together and there are other ways that you can multiply them. For example, you could use the foil method. And if you work at the foil method, you're gonna get the exact same result. The difference of squares provides a nice, simple, efficient way to get to the result. And without doing all of the steps of the foil method and having the possibility of making a sign error or a little addition error. But either way you'll get the same result. And that result is four M squared minus 100 N squared, which corresponds with answer choice B. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (8x + 7y)(8x − 7y)

Key Concepts

Product of Sum and Difference

Algebraic Expressions

Factoring and Expanding

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