GRE Quantitative: Algebra – Operations with Algebraic Expressions

One of the important sections in the GRE syllabus is the Quantitative Reasoning. After covering the topics of arithmetic, the next most prominent section asked in this section of the exam is algebra. Algebraic equations and its expressions are the topics that need to be mastered for the test day, since majority of the questions involve this topic in the exam.

This article will describe briefly about algebraic expressions.

Any mathematical expression that includes one or more than one variable is known as algebraic expressions. Certain letters are used for representing these variables, such as x, y, p, q, r… etc.

For example; 7 is a constant; it is not a variable. Any of the numbers can be a constant, like 7.2, 3/7,-√5, etc. all are constants. Whereas a variable does not hold any fixed value, it is changeable and is represented by an alphabet. Commonly the letters used for representing variables are p, q, and r; x, y, and z and a, b, and c. But it can be represented by any letter. The only reason of using a variable is for generalizing the result of an equation.

After variable and constants, next comes the standard operation that includes addition, subtraction, multiplication, and division. Putting all these three together, variable, constants and operations, gives us the algebraic expressions.

One of the easiest and least time-taking methods to solve algebraic expressions is FOIL method.

So, what is FOIL method?

Most of us would have studied this approach in our grade school, but with time and no practice, this approach has been long forgotten.

In FOIL method, FOIL stands for:

F- First

O- Outer

I- Inner

L- Last.

And it refers to the position of variables and/or numbers within the parenthesis.


Let’s understand this methodology in detail through this example:

Suppose we need to find the value of, (a-b) × (a+b)

Tip: Remember, parenthesis stands for multiplication.

Now, the tricky part is, how to solve a bunch of a’s and b’s. So, the answer to solving it is the FOIL method.

Let’s solve it now.

  • F (First): Since the first term in each of the parentheses is a, so multiply the a’s together which gives us: a2
  • (Outer): The term near the beginning of the left parenthesis is ‘a’ and near the end of right parenthesis is ‘b.’ Multiply these two together getting the value: ab
  • I (Inner): Next, multiply the inner terms together from each parenthesis: ({-b}×a) = -ab
  • L (Last): Finally, multiply the terms which are present at the rightmost of both the parenthesis to get: b2.

Follow this method and solving algebraic equations will be fun and easy.

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