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10th Grade Expanding Expressions (Distributive Property) Worksheet — Level 3 — Practice Set 2 — Answers

Answer sheet with worked solutions for the 10th Grade algebraic expressions worksheet.

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10th 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 − 2)(3x − 6)

Answer: 9x2 − 24x + 12

  1. 3x × 3x = 9x2
  2. 3x × −6 + −2 × 3x = −18x + −6x = −24x
  3. −2 × −6 = 12
2.Expand and simplify: (3x − 4)(x + 1)

Answer: 3x2 − x − 4

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

Answer: 3x2 + 22x + 35

  1. 3x × x = 3x2
  2. 3x × 5 + 7 × x = 15x + 7x = 22x
  3. 7 × 5 = 35
4.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
5.Expand and simplify: (3x + 4)(3x + 1)

Answer: 9x2 + 15x + 4

  1. 3x × 3x = 9x2
  2. 3x × 1 + 4 × 3x = 3x + 12x = 15x
  3. 4 × 1 = 4
6.Expand and simplify: (2x + 6)(2x − 4)

Answer: 4x2 + 4x − 24

  1. 2x × 2x = 4x2
  2. 2x × −4 + 6 × 2x = −8x + 12x = 4x
  3. 6 × −4 = −24
7.Expand and simplify: (4x − 7)(2x + 1)

Answer: 8x2 − 10x − 7

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

Answer: 9x2 − 12x + 3

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

Answer: 8x2 − 22x − 21

  1. 4x × 2x = 8x2
  2. 4x × −7 + 3 × 2x = −28x + 6x = −22x
  3. 3 × −7 = −21
10.Expand and simplify: (3x + 3)(x + 4)

Answer: 3x2 + 15x + 12

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

Answer: 8x2 + 8x − 16

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

Answer: 8x2 + 14x − 4

  1. 4x × 2x = 8x2
  2. 4x × 4 + −1 × 2x = 16x + −2x = 14x
  3. −1 × 4 = −4
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