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.

(x + 4)(x − 4)

Accepted Answer

Hello, everyone. We're gonna perform multiplication on the given expression. Open parentheses. A plus nine, close parentheses multiplied by open parentheses. A -9 closed parentheses. Our answer choices are A A squared minus 18, A plus BA 2 - C A squared plus 18 A plus D A squared plus rewriting my binomials. I again have open parentheses. A plus nine closed parentheses multiplied by open parentheses. A -9 closed parentheses. Recall that when you multiply two binomials, typically you would use the foil method which stands for first, outer, inner and last looking at the binomials we're given here. I recognize that I have the same terms with the opposite signs in both of these parentheses. This is a special case that results in the difference of two squares. What that means is that when we do foil, the middle terms would cancel out. So we don't need to multiply the middle terms because we have the exact same terms. But with different signs, all we need to multiply are the first terms. So a multiplied by A which is A squared in the last terms, nine multiplied by -9 to result in -81. This gives me the expression A squared -81. Knowing that this is supposed to be the difference of two squares. I do a quick check to make sure I have a minus sign in between my terms. And this is the product of this multiplication A squared minus 81 which is answer choice B have a nice day.

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (x + 4)(x − 4)

Key Concepts

Product of Sum and Difference

Binomial Multiplication

Difference of Squares

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