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.x²y² - 1

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 U squared K squared minus four. Our answer choices are a, the parentheses UK minus two, multiplied by the parentheses, UK plus two B UK multiplied by the parentheses, UK -4 C, the parentheses UK minus four multiplied by the parentheses, UK plus four D UK multiplied by the parentheses UK -2. Our original expression again was U squared K squared minus four. Even though our first term has two variables, it is still a perfect square as if I were to take the square root of it, I would end up with an exact number. I would not end up with a decimal or a fraction. So being the difference of two squares, I'm going to open two sets of parentheses next to each other. They are currently empty. And then I recall that the first term in each of my new parentheses is gonna be the square root of the first term of the difference of two squares. So the square root of U squared K squared, the squared of U is U, I'm sorry, squared of U squared is U, the square root of K squared is K. So UK is the first term in each new binomial. Then I take the square to the last term in the difference of two squares. And that's my last term in each of my new binomials. So the square to four is two. And so that is the second term in both binomials. Next, I recall that they need to have opposite signs. So my first set of parentheses has a minus sign in between the terms. My second set of parentheses has a plus sign in between the terms at this step. My factorization is the parentheses UK minus two, multiplied by the parentheses UK plus two. I have no other difference of squares. I have no other things I can factor. So this is my solution and it is answer choice a have a nice day.

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In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers.x²y² - 1

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