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

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

1.Expand and simplify: (2x + 4)(3x + 4)

Answer: 6x2 + 20x + 16

  1. 2x × 3x = 6x2
  2. 2x × 4 + 4 × 3x = 8x + 12x = 20x
  3. 4 × 4 = 16
2.Expand and simplify: (2x − 7)(2x − 4)

Answer: 4x2 − 22x + 28

  1. 2x × 2x = 4x2
  2. 2x × −4 + −7 × 2x = −8x + −14x = −22x
  3. −7 × −4 = 28
3.Expand and simplify: (2x + 4)(3x + 7)

Answer: 6x2 + 26x + 28

  1. 2x × 3x = 6x2
  2. 2x × 7 + 4 × 3x = 14x + 12x = 26x
  3. 4 × 7 = 28
4.Expand and simplify: (2x + 5)(3x − 2)

Answer: 6x2 + 11x − 10

  1. 2x × 3x = 6x2
  2. 2x × −2 + 5 × 3x = −4x + 15x = 11x
  3. 5 × −2 = −10
5.Expand and simplify: (4x − 5)(2x + 5)

Answer: 8x2 + 10x − 25

  1. 4x × 2x = 8x2
  2. 4x × 5 + −5 × 2x = 20x + −10x = 10x
  3. −5 × 5 = −25
6.Expand and simplify: (3x − 5)(x − 3)

Answer: 3x2 − 14x + 15

  1. 3x × x = 3x2
  2. 3x × −3 + −5 × x = −9x + −5x = −14x
  3. −5 × −3 = 15
7.Expand and simplify: (4x + 4)(2x + 5)

Answer: 8x2 + 28x + 20

  1. 4x × 2x = 8x2
  2. 4x × 5 + 4 × 2x = 20x + 8x = 28x
  3. 4 × 5 = 20
8.Expand and simplify: (4x − 1)(2x + 3)

Answer: 8x2 + 10x − 3

  1. 4x × 2x = 8x2
  2. 4x × 3 + −1 × 2x = 12x + −2x = 10x
  3. −1 × 3 = −3
9.Expand and simplify: (3x − 1)(x + 4)

Answer: 3x2 + 11x − 4

  1. 3x × x = 3x2
  2. 3x × 4 + −1 × x = 12x + −x = 11x
  3. −1 × 4 = −4
10.Expand and simplify: (4x − 5)(3x − 7)

Answer: 12x2 − 43x + 35

  1. 4x × 3x = 12x2
  2. 4x × −7 + −5 × 3x = −28x + −15x = −43x
  3. −5 × −7 = 35
11.Expand and simplify: (2x + 7)(2x − 4)

Answer: 4x2 + 6x − 28

  1. 2x × 2x = 4x2
  2. 2x × −4 + 7 × 2x = −8x + 14x = 6x
  3. 7 × −4 = −28
12.Expand and simplify: (2x + 7)(3x + 3)

Answer: 6x2 + 27x + 21

  1. 2x × 3x = 6x2
  2. 2x × 3 + 7 × 3x = 6x + 21x = 27x
  3. 7 × 3 = 21
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