The area of Mr. Smith's rectangular classroom is x² - 25. Which of the following binomials could represent the length and the width of the room?

Since area of a rectangle is found through multiplying length by width, we required to ?nd the factors in which multiply out to yield x² - 25. Because x² and 25 are both perfect squares (x² +   x • x and 25 = 5 • 5), the product, x² - 25, is known as a difference of two perfect squares, and its factors are the sum and difference of the square roots of its terms. Thus, because the square root of x² = x and the square root of 25 + 5, x² - 25   (x +   5)(x - 5).