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Combining Like Terms Help

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By — McGraw-Hill Professional
Updated on Sep 22, 2011

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.

Combining Like Terms

Table 7-1 Identification of 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

Combining Like Terms

Example 2

Subtract 8x – 5x.

Solution 2

Combining Like Terms

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

Example 3

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

Solution 3

Combining Like Terms

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

Combining Like Terms

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

Removing Parentheses and Combining Like Terms

Example 2

Simplify –2(x + 7y) + 6x.

Solution 2

Removing Parentheses and Combining Like Terms

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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