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9th Grade Expanding Expressions (Distributive Property) Worksheet — Level 3 — Practice Set 2 — 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 — Practice Set 2 — Answers

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

1.Expand and simplify: (3x + 7)(x + 1)

Answer: 3x2 + 10x + 7

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

Answer: 6x2 − 17x + 12

  1. 3x × 2x = 6x2
  2. 3x × −3 + −4 × 2x = −9x + −8x = −17x
  3. −4 × −3 = 12
3.Expand and simplify: (3x − 2)(2x − 2)

Answer: 6x2 − 10x + 4

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

Answer: 3x2 − 10x − 25

  1. 3x × x = 3x2
  2. 3x × −5 + 5 × x = −15x + 5x = −10x
  3. 5 × −5 = −25
5.Expand and simplify: (3x + 6)(x + 2)

Answer: 3x2 + 12x + 12

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

Answer: 12x2 − 8x − 20

  1. 4x × 3x = 12x2
  2. 4x × −5 + 4 × 3x = −20x + 12x = −8x
  3. 4 × −5 = −20
7.Expand and simplify: (2x + 6)(2x + 7)

Answer: 4x2 + 26x + 42

  1. 2x × 2x = 4x2
  2. 2x × 7 + 6 × 2x = 14x + 12x = 26x
  3. 6 × 7 = 42
8.Expand and simplify: (4x + 6)(2x − 5)

Answer: 8x2 − 8x − 30

  1. 4x × 2x = 8x2
  2. 4x × −5 + 6 × 2x = −20x + 12x = −8x
  3. 6 × −5 = −30
9.Expand and simplify: (4x − 1)(x + 1)

Answer: 4x2 + 3x − 1

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

Answer: 2x2 + 2x − 4

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

Answer: 4x2 + 12x + 9

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

Answer: 3x2 − 4x − 4

  1. 3x × x = 3x2
  2. 3x × −2 + 2 × x = −6x + 2x = −4x
  3. 2 × −2 = −4
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