In Exercises 1–22, factor each difference of two squares. Assume ...

Question

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers.

x² - 4

Accepted Answer

Hello, everyone. The following expression is a special product called the difference of two squares. We're gonna factorize it. The expression we're given is K squared minus nine. Our answer choices are a open parentheses, K minus three closed parentheses multiplied by open parentheses. K plus three closed parentheses. B open parentheses, three minus K closed parentheses multiplied by open parentheses. Three plus K closed parentheses. C K multiplied by open parentheses, K -9 closed parentheses. D. Open Parentheses, K - closed parentheses multiplied by open parentheses. K -3 closed parentheses. Right? We are told that our expression K squared minus nine is the difference of two squares. This happens when both terms in our binomial are perfect squares. There's a special format to factor this and in that format, we're gonna factor into two binomials. So I'm opening two empty sets of parentheses next to each other. The format for this factorization is to take the square root of the first term of the difference of two squares. So the square root of K squared which is K and that's the first term in each of our new binomials. The second term in our binomials comes from the square root of the second term in the difference of two squares. So the square root of nine, which is three. So in both sets of parentheses, my second term is three. Notice that at this point, we do not have any signs between the K and the three, this is because with the difference of two squares, we need to have opposite signs, meaning one set of parentheses gets a minus sign, The other set of parentheses gets a plus sign. So when this is completely factored, we are left with open parentheses, K minus three, closed parentheses multiplied by open parentheses. K plus three closed parentheses. That is our factorization and answer choice. I have a nice day.

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers. x² - 4

Key Concepts

Difference of Squares

Factoring

Exponents

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