15-Read the following SAT test question, then click on a button to select your answer.

If x + y = 3 and x – y = 5, then x2 – y2 =

A. 4
B. 8
C. 15
D. 16
E. 64




Correct Answer: C

* Here's Why:

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.
* Difficulty: Medium
* Question Type: Standard Multiple Choice
(Mathematics)