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9th Grade Expanding Expressions (Distributive Property) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the 9th Grade algebraic expressions worksheet.

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9th Grade Expanding Expressions (Distributive Property) Worksheet — Level 3 — Answers

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

1.Expand and simplify: (2x + 6)(x − 4)

Answer: 2x2 − 2x − 24

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

Answer: 6x2 − 19x − 7

  1. 2x × 3x = 6x2
  2. 2x × 1 + −7 × 3x = 2x + −21x = −19x
  3. −7 × 1 = −7
3.Expand and simplify: (2x − 7)(2x − 2)

Answer: 4x2 − 18x + 14

  1. 2x × 2x = 4x2
  2. 2x × −2 + −7 × 2x = −4x + −14x = −18x
  3. −7 × −2 = 14
4.Expand and simplify: (4x + 5)(2x + 6)

Answer: 8x2 + 34x + 30

  1. 4x × 2x = 8x2
  2. 4x × 6 + 5 × 2x = 24x + 10x = 34x
  3. 5 × 6 = 30
5.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
6.Expand and simplify: (4x − 5)(2x − 5)

Answer: 8x2 − 30x + 25

  1. 4x × 2x = 8x2
  2. 4x × −5 + −5 × 2x = −20x + −10x = −30x
  3. −5 × −5 = 25
7.Expand and simplify: (2x − 5)(2x − 6)

Answer: 4x2 − 22x + 30

  1. 2x × 2x = 4x2
  2. 2x × −6 + −5 × 2x = −12x + −10x = −22x
  3. −5 × −6 = 30
8.Expand and simplify: (4x + 3)(3x − 1)

Answer: 12x2 + 5x − 3

  1. 4x × 3x = 12x2
  2. 4x × −1 + 3 × 3x = −4x + 9x = 5x
  3. 3 × −1 = −3
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: (3x − 2)(2x − 3)

Answer: 6x2 − 13x + 6

  1. 3x × 2x = 6x2
  2. 3x × −3 + −2 × 2x = −9x + −4x = −13x
  3. −2 × −3 = 6
11.Expand and simplify: (2x − 7)(2x + 2)

Answer: 4x2 − 10x − 14

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

Answer: 4x2 + 20x + 21

  1. 2x × 2x = 4x2
  2. 2x × 7 + 3 × 2x = 14x + 6x = 20x
  3. 3 × 7 = 21
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