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Combining Like Terms

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**Like terms have the same variable raised to the same power.**

Combining Like Terms Like terms have the same variable raised to the same power. Why don’t we take a look at examples and non-examples of like terms? EXAMPLES NON-EXAMPLES 5x 3x 10x 11x 2x The terms are NOT alike since the exponents are not the same. The terms are alike since every term has “x” to the 1st power. The terms are alike since every term has “a” to the 2nd power. The terms are NOT alike since the letters are not the same.

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**Example #1 Simplify the given expression:**

1st Step: Identify the like terms. 8a and 4a are alike since they both contain “a” to the 1st power. 2b and 5b are alike since they both contain “b” to the 1st power. 2nd step: Re-Write the problem with the like terms next to each other. 8a and 4a are next to one another 2b and 5b are next to one another 3rd step: Combine the Like Terms. 12a + 7b is the final answer. These 2 terms cannot be combined since they contain different variables.

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**Example #2 Simplify the given expression:**

1st Step 1: Identify the like terms. 5x and 2x are alike since they both contain “x” to the 1st power. 6y and y are alike since they both contain “y” to the 1st power. 8 and -3 are alike since they are constants (Constants contain no variables). 2nd step: Re-Write the problem with the like terms next to each other. Please notice that there is a minus sign in front of 3. Keep the minus with the 3 when rewriting problem. 5x and 2x are next to one another 6y and y are next to one another 8 and -3 are next to one another 3rd step: Combine the Like Terms. 7x + 7y + 5 is the final answer. These three terms cannot be combined, they are not alike. They contain different variables or they are constants. 6y+ y=7y because y is the same as 1y

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**Example #3 Simplify the given expression:**

1st Step 1: Identify the like terms. 2nd step: Re-Write the problem with the like terms next to each other. That is your final answer. These three terms cannot be combined, they are not alike. They contain variables to a different power or they are constants. 3rd step: Combine the Like Terms.

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Example #4 Simplify the expression 4b b + 2 and evaluate for b = 3 1st Step 1: Identify the like terms. 4b and 6b are alike since they both contain “b” to the 1st power. 5 and 2 are alike since they are constants. (Constants contain no variables). Step 2: Re-Write the problem with the like terms next to each other. 4b and 6b are next to one another 5 and 2 are next to one another 10b + 7 is the simplified expression. These two terms cannot be combined, they are not alike. Step 3: Combine the Like Terms. Step 4: Substitute or “plug” 3 in for b and simplify. Final Answer 10b means 10 times b, so when we replace b with 3, we multiply 10 times 3.

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Example #5 Simplify the expression 2x x – 2 + 4y + 2y and evaluate for x = 3 and y=2 1st Step 1: Identify the like terms. 2x and 3x are alike since they both contain “x” to the 1st power. 4y and 2y are alike since they both contain “y” to the 1st power. 6 and -2 are alike since they are constants. (Constants contain no variables). Step 2: Re-Write the problem with the like terms next to each other. Please notice that there is a minus sign in front of 2. Keep the minus with the 2 when rewriting problem=) 2x and 3x are next to one another 6 and -2 are next to one another 4y and 2y are next to one another 5x + 6y + 4 is the simplified expression. These three terms cannot be combined, they are not alike. Step 3: Combine the Like Terms.

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Example #5….continued Step 4: Plug 3 in for x and 2 in for y….and then simplify. 6y means 6 times y, so when we replace y with 2, we multiply 6 times 2. 5x means 5 times x, so when we replace x with 3, we multiply 5 times 3. Final Answer

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10.4 Addition and Subtraction: Like Denominators.

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