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 =

1. 4
   
   
2. 8
   
   
3. 15
   
   
4. 16
   
   
5. 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