# Equations

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

Read the question carefully, identify the bottom line (what the question is asking), and assess your options for solving it. You want to be as efficient as possible when solving math questions, so for most problems you should not look at the multiple choice answers before attacking the problem with the method you have chosen. Always loop back at the end of the problem to make sure that your answer addresses the bottom line.

If $(t-2)^{2}=0$, what is the value of (t + 3)(t + 6)?

You must find the value of (t - 3)(t + 6). In order to do this, you must first find the value of t. Paraphrase the question in your mind: “If this is true, then solve this.” This question is already set up in two steps for you.  Solve the first equation and you will have the key to solving the second part of the problem because there is only one variable involved: t.

Think about the first equation logically. Something squared is equal to zero, so what can be multiplied by itself and equal zero? The only possible answer is zero! The squared portion of the problem must be equal to zero.

$(t-2)^{2}=0$ and $0^{2}=0$, therefore t - 2 = 0.

When you add the 2 to both sides of your new equation, you will see that = 2. Now that you know the value of t, you have all the information that you need to solve the second part of the problem with simple arithmetic.

(t + 3)(t + 6)

(2 + 3)(2 + 6)

(5)(8)

40

Loop back to make sure that the answer you found answers the question you were asked. The problem asked for the value of (t + 3)(t + 6), and that is exactly what you found. Finally, match your answer to the correct answer choice.

(A) 40

(B) 18

(C) 9

(D) 4

(E) It cannot be determined from the information given.