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8th Grade Factoring Expressions (Common Factors) Worksheet — Level 2 — Answers

Answer sheet with worked solutions for the 8th Grade algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheet8th Grade · Mathematics · Algebraic Expressions

8th Grade Factoring Expressions (Common Factors) Worksheet — Level 2 — Answers

Find the highest common factor of the terms and write it outside the parentheses.

1.Factor fully: 3x − 3y

Answer: 3(x − y)

  1. Highest common factor: 3
  2. 3x − 3y = 3(x − y)
  3. Check by expanding the parentheses.
2.Factor fully: 15x2 + 25x

Answer: 5x(3x + 5)

  1. Highest common factor: 5x
  2. 15x2 + 25x = 5x(3x + 5)
  3. Check by expanding the parentheses.
3.Factor fully: 16x + 40y

Answer: 8(2x + 5y)

  1. Highest common factor: 8
  2. 16x + 40y = 8(2x + 5y)
  3. Check by expanding the parentheses.
4.Factor fully: 20x2 − 28x

Answer: 4x(5x − 7)

  1. Highest common factor: 4x
  2. 20x2 − 28x = 4x(5x − 7)
  3. Check by expanding the parentheses.
5.Factor fully: 42a + 35b

Answer: 7(6a + 5b)

  1. Highest common factor: 7
  2. 42a + 35b = 7(6a + 5b)
  3. Check by expanding the parentheses.
6.Factor fully: 24x2 − 30x

Answer: 6x(4x − 5)

  1. Highest common factor: 6x
  2. 24x2 − 30x = 6x(4x − 5)
  3. Check by expanding the parentheses.
7.Factor fully: 2x − 14y

Answer: 2(x − 7y)

  1. Highest common factor: 2
  2. 2x − 14y = 2(x − 7y)
  3. Check by expanding the parentheses.
8.Factor fully: 8x2 − 36x

Answer: 4x(2x − 9)

  1. Highest common factor: 4x
  2. 8x2 − 36x = 4x(2x − 9)
  3. Check by expanding the parentheses.
9.Factor fully: 8x + 20y

Answer: 4(2x + 5y)

  1. Highest common factor: 4
  2. 8x + 20y = 4(2x + 5y)
  3. Check by expanding the parentheses.
10.Factor fully: 6x2 + 24x

Answer: 6x(x + 4)

  1. Highest common factor: 6x
  2. 6x2 + 24x = 6x(x + 4)
  3. Check by expanding the parentheses.
11.Factor fully: 5m − 35n

Answer: 5(m − 7n)

  1. Highest common factor: 5
  2. 5m − 35n = 5(m − 7n)
  3. Check by expanding the parentheses.
12.Factor fully: 6x2 + 3x

Answer: 3x(2x + 1)

  1. Highest common factor: 3x
  2. 6x2 + 3x = 3x(2x + 1)
  3. Check by expanding the parentheses.
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