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9th Grade Expanding Expressions (Distributive Property) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers

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

1.Expand and simplify: (4x − 1)(x − 1)

Answer: 4x2 − 5x + 1

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

Answer: 9x2 + 9x − 4

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

Answer: 3x2 − 9x + 6

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

Answer: 2x2 + 13x + 15

  1. 2x × x = 2x2
  2. 2x × 5 + 3 × x = 10x + 3x = 13x
  3. 3 × 5 = 15
6.Expand and simplify: (2x − 6)(2x + 3)

Answer: 4x2 − 6x − 18

  1. 2x × 2x = 4x2
  2. 2x × 3 + −6 × 2x = 6x + −12x = −6x
  3. −6 × 3 = −18
7.Expand and simplify: (3x + 4)(2x − 6)

Answer: 6x2 − 10x − 24

  1. 3x × 2x = 6x2
  2. 3x × −6 + 4 × 2x = −18x + 8x = −10x
  3. 4 × −6 = −24
8.Expand and simplify: (4x + 2)(3x − 2)

Answer: 12x2 − 2x − 4

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

Answer: 12x2 + 3x − 42

  1. 4x × 3x = 12x2
  2. 4x × 6 + −7 × 3x = 24x + −21x = 3x
  3. −7 × 6 = −42
10.Expand and simplify: (3x + 4)(x + 5)

Answer: 3x2 + 19x + 20

  1. 3x × x = 3x2
  2. 3x × 5 + 4 × x = 15x + 4x = 19x
  3. 4 × 5 = 20
11.Expand and simplify: (4x − 7)(x + 7)

Answer: 4x2 + 21x − 49

  1. 4x × x = 4x2
  2. 4x × 7 + −7 × x = 28x + −7x = 21x
  3. −7 × 7 = −49
12.Expand and simplify: (2x − 5)(3x − 1)

Answer: 6x2 − 17x + 5

  1. 2x × 3x = 6x2
  2. 2x × −1 + −5 × 3x = −2x + −15x = −17x
  3. −5 × −1 = 5
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