Question

Find a pair of factors for each number by using the difference of two squares.

a. 45
b. 77
c. 112

Answer 1

The answers are:
a) 9 and 5
b) 11 and 7
c) 14 and 8


a² - b² = (a + b)(a - b)

a) The answer is 9 and 5

45= a² - b²
45 = 49 - 4 = 7² - 2² = (7 + 2)(7 - 2) = 9 * 5


b) The answer is 11 and 7

77 = a² - b²
77 = 81 - 4 = 9² - 2² = (9 + 2)(9 - 2) = 11 * 7


c) The answer is 14 and 8

112 = a² - b²
112 = 121 - 9 = 11² - 3² = (11 + 3)(11 - 3) = 14 * 8