Transcript If x + y = 3 and x – y = 5, then x2 – y2 = Difficulty: Medium a) 4 b) 8 c)

If x + y = 3 and x – y = 5, then x2 – y2 =
Difficulty: Medium
a) 4
b) 8
c) 15
d) 16
e) 64
HINT
If you factor x2 – y2, you can find its value as (x + y)(x – y).
C: 15
Explanation
Recall that x2 – y2 can be factored as (x + y)(x – y). Since x + y = 3 and x – y =
5, their product, x2 – y2, is (3)(5), or 15.
Another method of solution is to solve the two
equations x + y = 3 and x – y = 5 simultaneously to get x = 4 and y = –1. Then
x2 – y2 is 42 – (–1)2 = 16 – 1 = 15.