Algebra

10/9 Algebra

Read the following SAT test question and then select the correct answer.

Read each question carefully.  Then identify the bottom line and assess your options for finding it.  Choose the most efficient method to attack the problem.  Before selecting your answer, loop back to make sure that you solved for the bottom line; you do not want to give the answer for x when your problem asks for something else entirely!

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

Bottom Linex² - y² = ?

Assess your options: For this problem, noting your bottom line can save you a lot of time!  Most people are going to solve for x and y, but your bottom line is really x² - y².  You do not need to know what x and y equal to solve this problem.  If you solve for your bottom line rather than solving for x and y, you can save time on this problem and have more time for other problems during your SAT test.

Attack the problemx² - y² is one of three key quadratic equations that you should have memorized.  It shows up on your Knowsys Formula chart as a² - b² = (a + b)(a – b).  If you have this memorized, you know that x² - y² = (x + y)(x – y).  You have already been given the values for both (x + y) and (x – y) in the question!  All you have to do is plug them in.  Then you have x² - y² = (x + y)(x – y) = (3)(5).  Your answer is 15.

Loop back:  This is the process that you just used:  x² - y² = (x + y)(x – y) = (3)(5) = 15.  You solved for the bottom line, so you are ready to look down at your answer choices.

(A) 4
(B) 8
(C) 15
(D) 16
(E) 64