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 + 5)(x − 5)

Accepted Answer

Hello, everyone. We are gonna perform multiplication on the given expression. Open parentheses. F plus 11 closed parentheses, multiplied by open parentheses. F minus 11 closed parentheses. Our answer choices are A F squared minus T 1 21 B F squared minus 22 F plus 121 C F squared plus D F squared plus 22 F plus rewriting our binomials. I have open parentheses. F plus 11, closed parentheses multiplied by open parentheses. F minus 11 closed parentheses. I recall that when I multiply two binomials, I typically use the foil method which stands for first, outer inner and last here, I recognize that both sets of parentheses have the same terms but with an opposite sign in between them, they're both F and 11 but one has a plus sign. One has a minus sign. I recall that this is a special case that will result in the difference of two squares. This means the middle terms will cancel out. So we no longer have to do all of foil. All we need to do is multiply the first terms and the last terms. So the first terms would be F multiplied by F which would give us F squared. The last terms are 11, multiplied by negative 11, which results in -121. And that's our product F squared minus 121. That's answer choice. A have a nice day.

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (x + 5)(x − 5)

Key Concepts

Product of Sum and Difference

Binomial Multiplication

Difference of Squares

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