Simplifying Algebraic Expressions Worksheet

Welcome to your expanded worksheet on simplifying algebraic expressions. In this section, you will find 20 problems that focus on combining like terms and using the distributive property. All expressions are designed so that none of the answers involve negative numbers. Remember to show all of your work as you simplify each expression.

Problem 1

Simplify the expression:

2x + 3x + 5

Your answer:

Problem 2

Simplify the expression:

4a + 2a + 7

Your answer:

Problem 3

Simplify the expression by applying the distributive property:

3(2x + 4)

Your answer:

Problem 4

Simplify the expression:

5y + 2y + 3

Your answer:

Problem 5

Simplify the expression:

7m + 5m + 10

Your answer:

Problem 6

Simplify the expression by applying the distributive property:

2(3a + 5)

Your answer:

Problem 7

Simplify the expression by applying the distributive property:

4(2y + 8)

Your answer:

Problem 8

Simplify the expression:

6z + 3z + 4

Your answer:

Problem 9

Simplify the expression:

8p + 3p + 12

Your answer:

Problem 10

Simplify the expression by using the distributive property:

5(2x + 3)

Your answer:

Problem 11

Simplify the expression by combining like terms:

9r + 4r + 1

Your answer:

Problem 12

Simplify the expression:

3(3b) + 2b

Your answer:

Problem 13

Simplify the expression by applying the distributive property:

3(2x + 6)

Your answer:

Problem 14

Simplify the expression:

2(4a + 3) + 3a

Your answer:

Problem 15

Simplify the expression by combining like terms:

10y + 4y + 8

Your answer:

Problem 16

Simplify the expression by applying the distributive property first:

3(4m + 2) + m

Your answer:

Problem 17

Simplify the expression:

5(3p) + 2p

Your answer:

Problem 18

Simplify the expression by applying the distributive property:

4(3z + 2) + z

Your answer:

Problem 19

Simplify the expression by combining like terms and applying the distributive property:

2(2x + 5) + 3x

Your answer:

Problem 20

Simplify the expression:

7a + 3 + 2(2a + 4)

Your answer:

Good luck, and remember to check your work carefully!

Simplifying Algebraic Expressions Answer Key

This answer key provides a detailed step-by-step explanation for simplifying each expression on the worksheet. Follow these steps to verify your work.

Problem 1

Expression: 2x + 3x + 5

Steps:

1. Identify like terms: 2x and 3x.
2. Add the coefficients: 2 + 3 = 5, so 2x + 3x = 5x.
3. The constant remains unchanged.

Final Answer: 5x + 5

Problem 2

Expression: 4a + 2a + 7

Steps:

1. Identify like terms: 4a and 2a.
2. Add the coefficients: 4 + 2 = 6, so 4a + 2a = 6a.
3. Include the constant 7.

Final Answer: 6a + 7

Problem 3

Expression: 3(2x + 4)

Steps:

1. Apply the distributive property: Multiply 3 by each term inside.
   • 3 × 2x = 6x
   • 3 × 4 = 12

Final Answer: 6x + 12

Problem 4

Expression: 5y + 2y + 3

Steps:

1. Identify like terms: 5y and 2y.
2. Add the coefficients: 5 + 2 = 7.
3. The constant remains 3.

Final Answer: 7y + 3

Problem 5

Expression: 7m + 5m + 10

Steps:

1. Identify like terms: 7m and 5m.
2. Add the coefficients: 7 + 5 = 12.
3. The constant is 10.

Final Answer: 12m + 10

Problem 6

Expression: 2(3a + 5)

Steps:

1. Distribute 2 over the parentheses:
   • 2 × 3a = 6a
   • 2 × 5 = 10

Final Answer: 6a + 10

Problem 7

Expression: 4(2y + 8)

Steps:

1. Apply the distributive property:
   • 4 × 2y = 8y
   • 4 × 8 = 32

Final Answer: 8y + 32

Problem 8

Expression: 6z + 3z + 4

Steps:

1. Combine like terms: 6z + 3z = 9z.
2. Add the constant 4.

Final Answer: 9z + 4

Problem 9

Expression: 8p + 3p + 12

Steps:

1. Combine like terms: 8p + 3p = 11p.
2. Append the constant 12.

Final Answer: 11p + 12

Problem 10

Expression: 5(2x + 3)

Steps:

1. Apply the distributive property:
   • 5 × 2x = 10x
   • 5 × 3 = 15

Final Answer: 10x + 15

Problem 11

Expression: 9r + 4r + 1

Steps:

1. Combine like terms: 9r + 4r = 13r.
2. Add the constant 1.

Final Answer: 13r + 1

Problem 12

Expression: 3(3b) + 2b

Steps:

1. Multiply: 3 × 3b = 9b.
2. Combine terms: 9b + 2b = 11b.

Final Answer: 11b

Problem 13

Expression: 3(2x + 6)

Steps:

1. Distribute 3:
   • 3 × 2x = 6x
   • 3 × 6 = 18

Final Answer: 6x + 18

Problem 14

Expression: 2(4a + 3) + 3a

Steps:

1. First distribute 2 over (4a + 3):
   • 2 × 4a = 8a
   • 2 × 3 = 6
2. Add 3a to the result: 8a + 3a = 11a.
3. Include the constant 6.

Final Answer: 11a + 6

Problem 15

Expression: 10y + 4y + 8

Steps:

1. Combine like terms: 10y and 4y gives 14y.
2. The constant is 8.

Final Answer: 14y + 8

Problem 16

Expression: 3(4m + 2) + m

Steps:

1. Apply the distributive property:
   • 3 × 4m = 12m
   • 3 × 2 = 6
2. Add m: 12m + m = 13m.

Final Answer: 13m + 6

Problem 17

Expression: 5(3p) + 2p

Steps:

1. Multiply: 5(3p) = 15p.
2. Combine like terms: 15p + 2p = 17p.

Final Answer: 17p

Problem 18

Expression: 4(3z + 2) + z

Steps:

1. Distribute 4:
   • 4 × 3z = 12z
   • 4 × 2 = 8
2. Add z to get: 12z + z = 13z.

Final Answer: 13z + 8

Problem 19

Expression: 2(2x + 5) + 3x

Steps:

1. Distribute 2: 2 × 2x = 4x, and 2 × 5 = 10.
2. Combine the resulting expression with 3x: 4x + 3x = 7x.
3. Include the constant 10.

Final Answer: 7x + 10

Problem 20

Expression: 7a + 3 + 2(2a + 4)

Steps:

1. Distribute 2 over (2a + 4):
   • 2 × 2a = 4a
   • 2 × 4 = 8
2. Combine like terms with 7a: 7a + 4a = 11a.
3. Add the constants: 3 + 8 = 11.

Final Answer: 11a + 11

Review each step to ensure you understand the process of simplifying algebraic expressions using combining like terms and the distributive property.