**Combining Like Terms**

**Like terms** have the same variables and the same exponents of the variables. For example, 3x and –5x are like terms because they have the same variables, whereas 5x and –8y are **unlike terms** because they have different variables. Table 7-1 will help you to identify like terms.

Like terms can be added or subtracted: e.g., 4x + 2x = 6x.

*To add or subtract like terms, add or subtract the numerical coefficients and use the same variables* .

**Examples**

**Example 1**

Add 7y + 3y.

**Solution 1**

**Example 2**

Subtract 8x – 5x.

**Solution 2**

Adding or subtracting like terms is often called "combining like terms."

**Example 3**

Combine like terms: 9x + 7x – 3x – 2x.

**Solution 3**

Unlike terms cannot be added or subtracted. When an expression has both like and unlike terms, it can be simplified by combining all like terms.

**Example 4**

Combine like terms: 6x – 8x + 2y – 3y + 5x – 4y.

**Solution 4**

**Math Note:** An algebraic expression of the form a +(-b) is usually written as a – b.

Find practice problems and solutions at Combining Like Terms Practice Problems - Set 1.

**Removing Parentheses and Combining Like Terms**

Sometimes in algebra it is necessary to use the distributive property to remove parentheses and then combine terms. This procedure is also called "simplifying" an algebraic expression.

**Examples**

**Example 1**

Simplify 5(2x + 3) – 6.

**Solution 1**

**Example 2**

Simplify –2(x + 7y) + 6x.

**Solution 2**

Find practice problems and solutions at Combining Like Terms Practice Problems - Set 2.

More practice problems for this concept can be found at: Expressions And Equations Practice Test.

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