Introduction

Combining like terms is one of the most important early skills in algebra.
It helps you simplify expressions so they are easier to understand and work with.

In this article, you will learn:

• What “like terms” are
• How to identify them
• How to combine them correctly
• Common mistakes to avoid
• Practice exercises to build confidence

What Are Like Terms?

Like terms are terms that have:

• The same variable, and
• The same exponent on that variable

Examples:

• $3x$ and $7x$ are like terms
• $5y$ and $-2y$ are like terms
• $4$ and $-9$ are like terms (constants)
• $2x$ and $2x^2$ are not like terms
• $3a$ and $3b$ are not like terms

Why Do We Combine Like Terms?

Combining like terms helps:

• Make expressions shorter
• Make equations easier to solve
• Reduce clutter
• Reveal structure in an expression

Think of it like tidying up a messy room—grouping similar items together.

How to Identify Like Terms

Look for:

• The same variable
• The same power
• The same structure

Examples of groups:

• $2x$, $-5x$, $10x$
• $3y^2$, $y^2$, $-8y^2$
• $4$, $-1$, $7$

How to Combine Like Terms

Once you identify like terms:

1. Add or subtract their coefficients
2. Keep the variable part the same

Examples:

• $3x + 5x = 8x$
• $7y - 2y = 5y$
• $4 + 9 = 13$
• $10x^2 - 6x^2 + x^2 = 5x^2$

Common Mistakes

• Mixing terms with different variables
  • Example: $3x + 4y$ cannot be combined
• Mixing terms with different exponents
  • Example: $x + x^2$ cannot be combined
• Forgetting negative signs
  • Example: $5x - 8x = -3x$

Practice Examples

Here are some simplified expressions to study:

• $3x + 2x = 5x$
• $7y - 4y + y = 4y$
• $9 + 3 - 5 = 7$
• $6a + 2b - a = 5a + 2b$

Calculator

Exercises

1. Simplify: $4x + 3x$

   Solution

   $4x + 3x = 7x$
   Add the coefficients: $4 + 3 = 7$.
2. Simplify: $7y - 2y + y$

   Solution

   $7y - 2y + y = 6y$
   Combine: $7 - 2 + 1 = 6$.
3. Combine like terms: $5 + 9 - 3$

   Solution

   $5 + 9 - 3 = 11$
   Combine constants: $14 - 3 = 11$.
4. Simplify: $6a + 2b - a$

   Solution

   $6a + 2b - a = 5a + 2b$
   Combine $6a - a = 5a$.
5. Simplify: $10x - 4x + 2x$

   Solution

   $10x - 4x + 2x = 8x$
   Combine: $10 - 4 + 2 = 8$.
6. True or false: $3x$ and $3x^2$ are like terms.

   Solution

   False.
   $3x$ and $3x^2$ have different exponents, so they are not like terms.
7. Simplify: $8 - 5 + 12$

   Solution

   $8 - 5 + 12 = 15$
   Combine: $3 + 12 = 15$.
8. Combine like terms: $9m + m - 4m$

   Solution

   $9m + m - 4m = 6m$
   Combine: $9 + 1 - 4 = 6$.