Combining Like Terms

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Combining Like Terms
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Combining Like Terms
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?
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 y7y 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 5 6b 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 6 3x 2 4y 2y
and evaluate for x 3 and y2
1st Step 1 Identify the like terms.
2x and 3x are alike since they both contain x
to the 1st power.
6 and -2 are alike since they are constants.
(Constants contain no variables).
4y and 2y are alike since they both contain y
to the 1st power.
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