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

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

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

Answer: 4x2 − 4

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

Answer: 8x2 + 20x + 12

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

Answer: 9x2 − 6x − 8

  1. 3x × 3x = 9x2
  2. 3x × −4 + 2 × 3x = −12x + 6x = −6x
  3. 2 × −4 = −8
4.Expand and simplify: (4x + 1)(x + 7)

Answer: 4x2 + 29x + 7

  1. 4x × x = 4x2
  2. 4x × 7 + 1 × x = 28x + x = 29x
  3. 1 × 7 = 7
5.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
6.Expand and simplify: (3x + 7)(x − 3)

Answer: 3x2 − 2x − 21

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

Answer: 12x2 − 5x − 25

  1. 4x × 3x = 12x2
  2. 4x × −5 + 5 × 3x = −20x + 15x = −5x
  3. 5 × −5 = −25
8.Expand and simplify: (3x + 5)(2x − 2)

Answer: 6x2 + 4x − 10

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

Answer: 4x2 − 19x + 12

  1. 4x × x = 4x2
  2. 4x × −4 + −3 × x = −16x + −3x = −19x
  3. −3 × −4 = 12
10.Expand and simplify: (4x − 3)(x − 3)

Answer: 4x2 − 15x + 9

  1. 4x × x = 4x2
  2. 4x × −3 + −3 × x = −12x + −3x = −15x
  3. −3 × −3 = 9
11.Expand and simplify: (2x + 7)(2x − 7)

Answer: 4x2 − 49

  1. 2x × 2x = 4x2
  2. 2x × −7 + 7 × 2x = −14x + 14x = 0
  3. 7 × −7 = −49
12.Expand and simplify: (2x + 6)(x + 1)

Answer: 2x2 + 8x + 6

  1. 2x × x = 2x2
  2. 2x × 1 + 6 × x = 2x + 6x = 8x
  3. 6 × 1 = 6
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