The area of Mr. Smith's rectangular classroom is x^{2 }- 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 x^{2} - 25. Because x^{2} and 25 are both perfect squares (x^{2} + x • x and 25 = 5 • 5), the product, x^{2 }- 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 x^{2 }= x and the square root of 25 + 5, x^{2} - 25 (x + 5)(x - 5).