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.36x² - 49y²

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 81 H squared minus 100 K squared. Our answer choices are A, the quan DH minus K multiplied by the quan D each plus 100 K B, the Kandi 81 H -100 K multiplied by the quan DH plus K see negative, the quan D nine K minus 10 H multiplied by the quantity nine K plus 10 H D negative multiplied by the quan D 10-K minus nine H multiplied by the quan D 10-K plus nine H. So I'm gonna start off by rewriting my original expression 81 H squared minus 100 K squared. We are told this is the difference of two squares. And when I look at it, I recognize that 81 is a perfect square as is 100. So recall that when you factor the difference of two squares, you're gonna factor one binomial into two binomials. And the format we follow to do that is in our new binomials. The first term in each binomial is the square root of the first term in our difference of two squares. So the square root of 81 squared is nine H because the square root of 81 is nine and the square root of H squared is H. The second term in our new binomials is from the square root of the second term in the difference of two squares. So the square root of 100 k squared, square root of 100 is 10 square root of K squared is K. So 10-K is the second term in both binomials. Next, we put a minus sign in one set of the parentheses and a plus sign in the other. So at this step in factorization, we have open parentheses, nine H minus 10-K closed parentheses multiplied by open parentheses, nine H plus 10-K closed parentheses, checking my answer choices. This does not look like any of my answer choices. Um But I noticed that answer choice D has the same numbers, but I need to go one step further. The step further, I'm going to go is to rearrange the terms within our parentheses. To do that with subtraction, I need to factor out a negative one. So in our first set of parentheses, I'm factoring out negative one and this will make it so I can flip the two terms. So I now have 10-K minus nine H in that first set of parentheses in our second set of parentheses. Since it's addition, we can just switch them without actually having to do any other math. Because addition can go in either order where subtraction cannot, I now have negative one multiplied by the quantity 10-K minus N H, I'm sorry, nine H multiplied by the quantity 10-K plus nine H and that matches answer choice. D have a nice day.

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers.36x² - 49y²

Key Concepts

Difference of Squares

Perfect Squares

Factoring Techniques

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