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8th Grade Expanding Expressions (Distributive Property) Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers

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

1.Expand and simplify: (3x − 1)(2x + 3)

Answer: 6x2 + 7x − 3

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

Answer: 8x2 − 2

  1. 4x × 2x = 8x2
  2. 4x × −1 + 2 × 2x = −4x + 4x = 0
  3. 2 × −1 = −2
3.Expand and simplify: (4x − 6)(2x − 2)

Answer: 8x2 − 20x + 12

  1. 4x × 2x = 8x2
  2. 4x × −2 + −6 × 2x = −8x + −12x = −20x
  3. −6 × −2 = 12
4.Expand and simplify: (3x − 3)(2x − 6)

Answer: 6x2 − 24x + 18

  1. 3x × 2x = 6x2
  2. 3x × −6 + −3 × 2x = −18x + −6x = −24x
  3. −3 × −6 = 18
5.Expand and simplify: (4x + 4)(3x + 1)

Answer: 12x2 + 16x + 4

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

Answer: 6x2 + 17x − 14

  1. 2x × 3x = 6x2
  2. 2x × −2 + 7 × 3x = −4x + 21x = 17x
  3. 7 × −2 = −14
7.Expand and simplify: (4x + 2)(2x + 5)

Answer: 8x2 + 24x + 10

  1. 4x × 2x = 8x2
  2. 4x × 5 + 2 × 2x = 20x + 4x = 24x
  3. 2 × 5 = 10
8.Expand and simplify: (4x − 4)(2x + 6)

Answer: 8x2 + 16x − 24

  1. 4x × 2x = 8x2
  2. 4x × 6 + −4 × 2x = 24x + −8x = 16x
  3. −4 × 6 = −24
9.Expand and simplify: (3x − 7)(2x + 4)

Answer: 6x2 − 2x − 28

  1. 3x × 2x = 6x2
  2. 3x × 4 + −7 × 2x = 12x + −14x = −2x
  3. −7 × 4 = −28
10.Expand and simplify: (4x − 3)(x + 6)

Answer: 4x2 + 21x − 18

  1. 4x × x = 4x2
  2. 4x × 6 + −3 × x = 24x + −3x = 21x
  3. −3 × 6 = −18
11.Expand and simplify: (3x + 6)(x + 7)

Answer: 3x2 + 27x + 42

  1. 3x × x = 3x2
  2. 3x × 7 + 6 × x = 21x + 6x = 27x
  3. 6 × 7 = 42
12.Expand and simplify: (3x − 4)(3x − 7)

Answer: 9x2 − 33x + 28

  1. 3x × 3x = 9x2
  2. 3x × −7 + −4 × 3x = −21x + −12x = −33x
  3. −4 × −7 = 28
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