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Combining Like Terms

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

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Example #1 Simplify the given expression: 1 st Step: Identify the like terms. 8a and 4a are alike since they both contain a to the 1 st power. 2b and 5b are alike since they both contain b to the 1 st power. 2 nd 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: 1 st Step 1: Identify the like terms. 5x and 2x are alike since they both contain x to the 1 st power. 6y and y are alike since they both contain y to the 1 st power. 2 nd step: Re-Write the problem with the like terms next to each other. 5x and 2x 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. 8 and -3 are alike since they are constants (Constants contain no variables). 6y and y are next to one another 8 and -3 are next to one another Please notice that there is a minus sign in front of 3. Keep the minus with the 3 when rewriting problem. 6y+ y=7y because y is the same as 1y

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Example #3 Simplify the given expression: 1 st Step 1: Identify the like terms. 2 nd step: Re-Write the problem with the like terms next to each other. 3rd step: Combine the Like Terms. 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.

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Example #4 Simplify the expression 4b b + 2 and evaluate for b = 3 1 st Step 1: Identify the like terms. 4b and 6b are alike since they both contain b to the 1 st power. Step 2: Re-Write the problem with the like terms next to each other. 4b and 6b are next to one another Step 3: Combine the Like Terms. 10b + 7 is the simplified expression. These two terms cannot be combined, they are not alike. 5 and 2 are alike since they are constants. (Constants contain no variables). 5 and 2 are next to one another 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 1 st Step 1: Identify the like terms. 2x and 3x are alike since they both contain x to the 1 st power. Step 2: Re-Write the problem with the like terms next to each other. 2x and 3x are next to one another Step 3: Combine the Like Terms. 5x + 6y + 4 is the simplified expression. These three terms cannot be combined, they are not alike. 6 and -2 are alike since they are constants. (Constants contain no variables). 6 and -2 are next to one another 4y and 2y are alike since they both contain y to the 1 st power. 4y and 2y are next to one another Please notice that there is a minus sign in front of 2. Keep the minus with the 2 when rewriting problem=)

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

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