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Equivalent expressions worksheet

Grade 6 math, Common Core 6.EE.A.3. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

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Equivalent expressions

Grade 6 math, Common Core 6.EE.A.3

Write an equivalent expression as asked.

  1. 1.
    Factor using the GCF: 72x + 8
  2. 2.
    Are 3(x + 3) and 3x + 9 equivalent?
  3. 3.
    Use the distributive property: 8(7a + 1)
  4. 4.
    Combine like terms: 3n + 1 + 8n + 9
  5. 5.
    Are 6(y + 2) and 6y + 12 equivalent?
  6. 6.
    Use the distributive property: 3(8a − 8)
  7. 7.
    Use the distributive property: 4(5a + 7)
  8. 8.
    Use the distributive property: 4(8y + 7)
  9. 9.
    Combine like terms: 5n + 7 + 7n + 8
  10. 10.
    Factor using the GCF: 7y + 35
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Equivalent expressions

Grade 6 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. 8(9x + 1)

    The GCF of 72 and 8 is 8

  2. 2. Yes

    3(x + 3) = 3x + 9

  3. 3. 56a + 8

    8 × 7a = 56a8 × 1 = 8

  4. 4. 11n + 10

    3n + 8n = 11n1 + 9 = 10

  5. 5. Yes

    6(y + 2) = 6y + 12

  6. 6. 24a − 24

    3 × 8a = 24a3 × 8 = 24

  7. 7. 20a + 28

    4 × 5a = 20a4 × 7 = 28

  8. 8. 32y + 28

    4 × 8y = 32y4 × 7 = 28

  9. 9. 12n + 15

    5n + 7n = 12n7 + 8 = 15

  10. 10. 7(y + 5)

    The GCF of 7 and 35 is 7

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About equivalent expressions

Equivalent expressions have the same value for every value of the variable. The distributive property turns 3(x + 4) into 3x + 12, and factoring turns it back. Combining like terms adds terms with the same variable part: 4y + 3y = 7y.

Worked example 1

Combine like terms: 3x + 9 + 5x + 9
  1. Step 1.3x + 5x = 8x
  2. Step 2.9 + 9 = 18

Answer: 8x + 18

Worked example 2

Use the distributive property: 9(2x − 8)
  1. Step 1.9 × 2x = 18x
  2. Step 2.9 × 8 = 72

Answer: 18x − 72

Worked example 3

Factor using the GCF: 25a + 35
  1. Step 1.The GCF of 25 and 35 is 5

Answer: 5(5a + 7)

Watch out for

  • Multiply every term inside the brackets: 3(x + 4) is 3x + 12, not 3x + 4.
  • Only like terms can be combined: 4y and 3y can, but 4y and 3 can’t.
  • To check, put in a number for the variable: both expressions should give the same result.

Practice equivalent expressions online

On StudyWiz, your kid can practice equivalent expressions with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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