STRATEGY: Upon reading any GRE Multiple Choice question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test values of x and y to test for equivalency.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also expand and simplify the given expression.
On test day, I would probably choose the latter approach, but I'm going to show both approaches.


APPROACH #1: Expand and simplify
Given:$(x + 1)(y + 1) – x – y$
Expand: $(xy + x + y + 1) – x – y =$
Simplify: $xy + 1$
Answer: B

APPROACH #2: Test for equivalency
Key concept: If two expressions are equivalent, they must evaluate to the same value for every possible value of x.
For example, since the expression 2x + 3x is equivalent to the expression 5x, the two expressions will evaluate to the same number for every value of x.
So, if x = 7, the expression 2x + 3x = 2(7) + 3(7) = 14 + 21 = 35, and the expression 5x = 5(7) = 35

Let's evaluate the given expression for $x = 1$ and $y = 1$.
We get: $(x + 1)(y + 1) – x – y =(1 + 1)(1 + 1) – 1 – 1 = 2$

We will now evaluate each answer choice for $x = 1$ and $y = 1$ and eliminate those that don't evaluate to $2$
A. $(1)(1) – 1 – 1 + 1 = 0$. Doesn't evaluate to $2$. ELIMINATE.
B. $xy + 1 = (1)(1) + 1 = 2$. KEEP
C. $–1 – 1 + 1 = -1$. Doesn't evaluate to $2$. ELIMINATE.
D. $1^2 + 1^2 – 1 = 1$. Doesn't evaluate to $2$. ELIMINATE.
E. $1$. Doesn't evaluate to $2$. ELIMINATE.
Answer: B