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8th Grade Expanding Expressions (Distributive Property) Worksheet — Level 3 — Practice Set 4 — Answers

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

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8th Grade Expanding Expressions (Distributive Property) Worksheet — Level 3 — Practice Set 4 — Answers

Multiply every term inside the parentheses. Then collect like terms.

1.Expand and simplify: (3x − 1)(x + 1)

Answer: 3x2 + 2x − 1

  1. 3x × x = 3x2
  2. 3x × 1 + −1 × x = 3x + −x = 2x
  3. −1 × 1 = −1
2.Expand and simplify: (3x + 3)(3x + 6)

Answer: 9x2 + 27x + 18

  1. 3x × 3x = 9x2
  2. 3x × 6 + 3 × 3x = 18x + 9x = 27x
  3. 3 × 6 = 18
3.Expand and simplify: (2x + 2)(2x − 6)

Answer: 4x2 − 8x − 12

  1. 2x × 2x = 4x2
  2. 2x × −6 + 2 × 2x = −12x + 4x = −8x
  3. 2 × −6 = −12
4.Expand and simplify: (3x − 7)(3x − 1)

Answer: 9x2 − 24x + 7

  1. 3x × 3x = 9x2
  2. 3x × −1 + −7 × 3x = −3x + −21x = −24x
  3. −7 × −1 = 7
5.Expand and simplify: (4x + 6)(3x + 2)

Answer: 12x2 + 26x + 12

  1. 4x × 3x = 12x2
  2. 4x × 2 + 6 × 3x = 8x + 18x = 26x
  3. 6 × 2 = 12
6.Expand and simplify: (3x + 5)(2x + 2)

Answer: 6x2 + 16x + 10

  1. 3x × 2x = 6x2
  2. 3x × 2 + 5 × 2x = 6x + 10x = 16x
  3. 5 × 2 = 10
7.Expand and simplify: (3x − 6)(2x + 7)

Answer: 6x2 + 9x − 42

  1. 3x × 2x = 6x2
  2. 3x × 7 + −6 × 2x = 21x + −12x = 9x
  3. −6 × 7 = −42
8.Expand and simplify: (2x − 6)(x − 5)

Answer: 2x2 − 16x + 30

  1. 2x × x = 2x2
  2. 2x × −5 + −6 × x = −10x + −6x = −16x
  3. −6 × −5 = 30
9.Expand and simplify: (3x + 2)(x + 7)

Answer: 3x2 + 23x + 14

  1. 3x × x = 3x2
  2. 3x × 7 + 2 × x = 21x + 2x = 23x
  3. 2 × 7 = 14
10.Expand and simplify: (2x − 6)(2x − 2)

Answer: 4x2 − 16x + 12

  1. 2x × 2x = 4x2
  2. 2x × −2 + −6 × 2x = −4x + −12x = −16x
  3. −6 × −2 = 12
11.Expand and simplify: (3x + 6)(3x − 7)

Answer: 9x2 − 3x − 42

  1. 3x × 3x = 9x2
  2. 3x × −7 + 6 × 3x = −21x + 18x = −3x
  3. 6 × −7 = −42
12.Expand and simplify: (3x − 3)(2x − 5)

Answer: 6x2 − 21x + 15

  1. 3x × 2x = 6x2
  2. 3x × −5 + −3 × 2x = −15x + −6x = −21x
  3. −3 × −5 = 15
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