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10th Grade Expanding Expressions (Distributive Property) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers

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

1.Expand and simplify: (3x − 6)(3x + 4)

Answer: 9x2 − 6x − 24

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

Answer: 2x2 − x − 3

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

Answer: 2x2 + 9x − 5

  1. 2x × x = 2x2
  2. 2x × 5 + −1 × x = 10x + −x = 9x
  3. −1 × 5 = −5
4.Expand and simplify: (3x + 4)(3x + 7)

Answer: 9x2 + 33x + 28

  1. 3x × 3x = 9x2
  2. 3x × 7 + 4 × 3x = 21x + 12x = 33x
  3. 4 × 7 = 28
5.Expand and simplify: (3x + 7)(3x − 1)

Answer: 9x2 + 18x − 7

  1. 3x × 3x = 9x2
  2. 3x × −1 + 7 × 3x = −3x + 21x = 18x
  3. 7 × −1 = −7
6.Expand and simplify: (4x − 3)(2x − 5)

Answer: 8x2 − 26x + 15

  1. 4x × 2x = 8x2
  2. 4x × −5 + −3 × 2x = −20x + −6x = −26x
  3. −3 × −5 = 15
7.Expand and simplify: (2x + 4)(x + 5)

Answer: 2x2 + 14x + 20

  1. 2x × x = 2x2
  2. 2x × 5 + 4 × x = 10x + 4x = 14x
  3. 4 × 5 = 20
8.Expand and simplify: (4x − 4)(3x − 1)

Answer: 12x2 − 16x + 4

  1. 4x × 3x = 12x2
  2. 4x × −1 + −4 × 3x = −4x + −12x = −16x
  3. −4 × −1 = 4
9.Expand and simplify: (2x − 7)(x + 5)

Answer: 2x2 + 3x − 35

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

Answer: 4x2 + 26x + 30

  1. 4x × x = 4x2
  2. 4x × 5 + 6 × x = 20x + 6x = 26x
  3. 6 × 5 = 30
11.Expand and simplify: (3x − 3)(x − 6)

Answer: 3x2 − 21x + 18

  1. 3x × x = 3x2
  2. 3x × −6 + −3 × x = −18x + −3x = −21x
  3. −3 × −6 = 18
12.Expand and simplify: (4x − 4)(2x + 6)

Answer: 8x2 + 16x − 24

  1. 4x × 2x = 8x2
  2. 4x × 6 + −4 × 2x = 24x + −8x = 16x
  3. −4 × 6 = −24
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