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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).
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