Combining Like Terms

Show your work for each problem.

1.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
. We add the coefficients and keep the variable .
2.
Simplify:
Answer: 5y
. We subtract the coefficients and keep the variable .
3.
Which expression shows like terms?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
and are like terms because they both have the variable with the same exponent (1).
4.
Simplify:
Answer: 5x
. Remember that has an invisible coefficient of 1.
5.
Simplify:
Answer: 8a
1. Are and like terms? (yes/no) yes
2. What is ? 8
3. What is the simplified expression? 8a
6.
Simplify:
Answer: 6x + 3y
. Only the terms can be combined.
7.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
. Remember .
8.
Simplify:
Answer: 7x - 4
1. Identify the x terms. What are they? 5x and 2x
2. Combine the x terms: 7x
3. Identify the constants. What are they? 3 and -7
4. Combine the constants: -4
5. Write the final simplified expression 7x - 4
9.
Simplify:
Answer: 6m
10.
Simplify:
Answer: x + 8y
1. Combine the x terms: x
2. Combine the y terms: 8y
3. Write the final expression x + 8y
11.
Which expression is fully simplified?
1. a)
2. b)
3. c)
4. d)
Answer:
is fully simplified because and are unlike terms. The other expressions still have like terms to combine.
12.
Simplify:
Answer: 6x^2 + 2x
. Note: and have different exponents, so they cannot be combined.
13.
Simplify:
Answer: 7a + b + 3
1. Combine the a terms: 7a
2. Combine the b terms: b
3. Combine the constants: 3
4. Write the final expression 7a + b + 3
14.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
15.
Simplify:
Answer: 8x^2 + 2x - 7
16.
Simplify:
Answer: 6x + 6
1. First, distribute the 2: 2x + 6
2. Now write the full expression: 2x + 6 + 4x
3. Combine like terms: 6x + 6