Question

Which of the following shows how the number 7 can be rewritten with the difference of squares identity?

1.(16 - 9) = (4 + 3)(4 - 3)
2.(18 - 11) = (9 + 6)(9 - 5)
3.(25 - 4) = (5 + 2)(5 - 2)
4.(16 - 9) = -1(4 + 3)(4 - 3)
5.(64 - 1) = (8 + 1)(8 - 1)

Answer 1

If we let x and y be the two numbers such that the difference of their squares will give 7, we have the equation,
x^2 - y^2 = (x + y)(x - y) = 7
From the given choices, the squares are 16 and 9 which are squares of 4 and 3, respectively. Therefore,
16 - 9 = (4 + 3)(4 - 3) = 7
Thus, the answer is letter A.