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

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

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

Answer: 8x2 − 4x − 24

  1. 4x × 2x = 8x2
  2. 4x × −4 + 6 × 2x = −16x + 12x = −4x
  3. 6 × −4 = −24
2.Expand and simplify: (2x + 6)(3x + 6)

Answer: 6x2 + 30x + 36

  1. 2x × 3x = 6x2
  2. 2x × 6 + 6 × 3x = 12x + 18x = 30x
  3. 6 × 6 = 36
3.Expand and simplify: (2x + 5)(x + 7)

Answer: 2x2 + 19x + 35

  1. 2x × x = 2x2
  2. 2x × 7 + 5 × x = 14x + 5x = 19x
  3. 5 × 7 = 35
4.Expand and simplify: (2x − 4)(3x − 1)

Answer: 6x2 − 14x + 4

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

Answer: 12x2 + 17x − 7

  1. 4x × 3x = 12x2
  2. 4x × −1 + 7 × 3x = −4x + 21x = 17x
  3. 7 × −1 = −7
6.Expand and simplify: (2x − 5)(2x − 2)

Answer: 4x2 − 14x + 10

  1. 2x × 2x = 4x2
  2. 2x × −2 + −5 × 2x = −4x + −10x = −14x
  3. −5 × −2 = 10
7.Expand and simplify: (3x − 5)(2x − 7)

Answer: 6x2 − 31x + 35

  1. 3x × 2x = 6x2
  2. 3x × −7 + −5 × 2x = −21x + −10x = −31x
  3. −5 × −7 = 35
8.Expand and simplify: (3x − 3)(2x − 4)

Answer: 6x2 − 18x + 12

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

Answer: 12x2 + 7x − 12

  1. 4x × 3x = 12x2
  2. 4x × 4 + −3 × 3x = 16x + −9x = 7x
  3. −3 × 4 = −12
10.Expand and simplify: (4x + 7)(2x − 6)

Answer: 8x2 − 10x − 42

  1. 4x × 2x = 8x2
  2. 4x × −6 + 7 × 2x = −24x + 14x = −10x
  3. 7 × −6 = −42
11.Expand and simplify: (2x + 7)(x − 4)

Answer: 2x2 − x − 28

  1. 2x × x = 2x2
  2. 2x × −4 + 7 × x = −8x + 7x = −x
  3. 7 × −4 = −28
12.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
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