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.(5x + 3)(5x − 3)

Accepted Answer

Hello, everyone. We are gonna perform multiplication on the given expression. Open parentheses, six D plus five, closed parentheses multiplied by open parentheses. Six D minus five closed parentheses. Our answer choices are a 36 D squared minus 60 D minus 25 B 36 d squared -25 C 36 D squared minus 60 D plus 25 D 36 D squared plus 25 rewriting the binomials, we were given six D plus five, multiplied by the parentheses, six D minus five. First thing I recall is that when I multiply two binomials, I typically would use the foil method. So I would multiply first outer, inner and last. However, before I start multiplying with that method, I recognize that both sets of parentheses have the same terms. But with the opposite sign in between, I recall that this is a special case that results in the difference of two squaress, meaning my middle terms cancel out. So instead of having to do all of foil, I need to just multiply the first terms together. So six D multiplied by six D, six times six is 36 D multiplied by D is D squared. And then I need to multiply the last terms together five multiplied by -5, which is -25. And knowing it results in the difference of two squares, I double check to make sure I have a minus sign in between. But 36 D squared minus is my product. It is my answer and it's 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.(5x + 3)(5x − 3)

Key Concepts

Product of Sum and Difference

Binomial Multiplication

Difference of Squares

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