# How to Evaluate an Algebraic Expression

Struggling in algebra? Not even sure what an expression actually is? This is probably the first time you’ve found alphabet letters randomly thrown into your math problems. Not sure what to do? Well, here’s the guide for you.

## Steps

1. 1
Understand what a variable is. Those random letters you see in your math problems are referred to as variables. Each variable stands for a number that you don’t know.
• Example: In 2x + 6, the x is the variable
2. 2
Understand what an algebraic expression is. An algebraic expression is a set of numbers and variables combined by any number of mathematical operations (addition, multiplication, exponents etc). Here are some examples:
• 2x + 3y is an expression. It’s built by adding the product of 2 and x to the product of 3 and y.
• 2x by itself is also an expression. It’s a number 2 and a variable x combined by the mathematical operation of multiplication.
3. 3
Understand what it means to evaluate an algebraic expression. To evaluate an algebraic expression means to plug in a given number in place of a variable which in turn means to replace the variable with the given number.

For example, if you’re asked to evaluate 2x + 6 when x = 3, all you have to do is - rewrite the expression by replacing every x with 3. So, you end up with 2(3) + 6.
• Solve what you ended up with:

2(3) + 6

= 2×3 + 6

= 6 + 6

= 12

So, 2x + 6 = 12 when x = 3
4. 4
Try evaluating expressions that contain more than one variable. This works exactly the same way as evaluating an algebraic expression having only one variable does; you just do the same process more than once.

Say you’re asked to evaluate 4x + 3y when x = 2 , y = 6
• Replace x with 2: 4(2) + 3y
• Replace y with 6: 4(2) + 3(6)
• Solve:

4×2 + 3×6

= 8 + 18

= 26

So, 4x + 3y = 26 when x = 2 and y = 6
5. 5
Try evaluating expressions involving exponents.

Find 7x2 - 12x + 13 where x = 4
• Plug 4 in: 7(4)2 - 12(4) + 13
• Follow your orders of operation: PEMDAS. Because solving exponents comes before multiplication, square the 4 first before doing your multiplication or division, and then do addition or subtraction.

So, solving the exponent gives, (4)2 = 16.

This step should lead you to the expression 7(16) - 12(4) + 13
• Multiply or Divide:

7×16 - 12×4 + 13

= 112 - 48 + 13