Simplifying Algebraic Expressions

Show your work for each problem.

1.
Which terms are like terms?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
and are like terms because both have the variable to the power of 1. The other pairs have different variables or different exponents.
2.
Simplify:
Answer: 9x
. We add the coefficients (6 + 3 = 9) and keep the variable .
3.
Simplify:
Answer: 3y
. We subtract the coefficients (8 - 5 = 3) and keep the variable .
4.
What is the coefficient in ?
1. a)
2. b)
3. c)
4. d)
Answer:
In , the coefficient is . It's the number that multiplies the variable .
5.
Simplify:
Answer: 9x
1. Are all three terms like terms? yes
2. Add the coefficients: 9
3. Write the simplified expression 9x
6.
Simplify:
Answer: 7a + 3b
. We combine . The stays separate because it has a different variable.
7.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
. We combine the x terms: . The constant is not a like term, so it stays.
8.
Simplify:
Answer: 2x + 6y
1. Identify the x terms 3x and -x
2. Combine the x terms: 2x
3. Identify the y terms 4y and 2y
4. Combine the y terms: 6y
5. Write the final simplified expression 2x + 6y
9.
Simplify:
Answer: 0
. When we subtract a term from itself, we get zero.
10.
Which expression is already in simplest form?
1. a)
2. b)
3. c)
4. d)
Answer:
is already simplified because and are different variables and cannot be combined. The other expressions all have like terms that can be combined.
11.
Simplify:
Answer: 4a + 3
1. Identify the variable terms 7a and -3a
2. Combine the variable terms: 4a
3. Identify the constants 5 and -2
4. Combine the constants: 3
5. Write the final answer 4a + 3
12.
Simplify:
Answer: x^2 + 8x
terms: . terms: . Answer:
13.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
terms: . terms: . Constant: . Answer:
14.
Simplify:
Answer: 2x^2 - 5x + 4
1. Identify the terms 5x^2 and -3x^2
2. Combine: 2x^2
3. Identify the terms 2x and -7x
4. Combine: -5x
5. What is the constant? 4
6. Write in standard form (highest power first) 2x^2 - 5x + 4
15.
Simplify:
Answer: -7m + 7n - 8
terms: . terms: . Constant: . Answer:
16.
Simplify:
Answer: x^2 + 5xy - 5
1. Identify the terms 3x^2 and -2x^2
2. Combine: x^2
3. Identify the terms 4xy and xy
4. Combine: 5xy
5. What is the constant? -5
6. Write the final answer x^2 + 5xy - 5