Don’t fall for the SAT tricks and traps. Here is a Math problem that is not as complicated as it looks:

*13. If x ^{2} +y^{2} = 87 and xy = 38, what is the value of (x + y)^{2}?*

*A) 87*

*B) 125*

*C) 163*

*D) 250*

*E) 361*

**Identify:** Let’s identify the problem type. There are variables in an equation, and it looks like I will need to manipulate those variables somehow. This must be an ALGEBRA problem.

**Set Up:** Write down what you know, even if you have to rewrite the question in a different way.

*x ^{2} + y^{2} = 87*

*xy =38*

Is there any way to substitute xy into the first equation? It looks like I can’t because the variables in the first equation are squared. Maybe they are related somehow? Let’s see what the problem is asking because that can give us a clue as to how to manipulate these equations.

*(x + y) ^{2}?*

Hey, I know, this expression can be expanded:

*(x + y) ^{2} = x^{2} + 2xy + y^{2}*

**Make Sure:** Make sure you are answering the right question and you haven’t missed a step. Regroup the terms.

* (x + y) ^{2} =( x^{2} + y^{2})+ 2xy*

**Execute:** Now, just substitute the given equations:

*(x + y) ^{2} =87 + 2(38)*

Solve arithmetic with a calculator.

*(x + y) ^{2} =163*

**Answer: C**

[Reference: Test 6G, Section 7, Problem 13]