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

a. 45

b. 77

c. 112

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