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

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

1.Expand and simplify: (4x + 3)(3x + 7)

Answer: 12x2 + 37x + 21

  1. 4x × 3x = 12x2
  2. 4x × 7 + 3 × 3x = 28x + 9x = 37x
  3. 3 × 7 = 21
2.Expand and simplify: (4x + 6)(x − 1)

Answer: 4x2 + 2x − 6

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

Answer: 4x2 + 6x − 4

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

Answer: 8x2 − 26x − 7

  1. 4x × 2x = 8x2
  2. 4x × −7 + 1 × 2x = −28x + 2x = −26x
  3. 1 × −7 = −7
5.Expand and simplify: (3x + 7)(3x + 4)

Answer: 9x2 + 33x + 28

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

Answer: 4x2 − 21x + 5

  1. 4x × x = 4x2
  2. 4x × −5 + −1 × x = −20x + −x = −21x
  3. −1 × −5 = 5
7.Expand and simplify: (4x − 2)(x + 2)

Answer: 4x2 + 6x − 4

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

Answer: 6x2 + 4x − 42

  1. 3x × 2x = 6x2
  2. 3x × 6 + −7 × 2x = 18x + −14x = 4x
  3. −7 × 6 = −42
9.Expand and simplify: (3x − 4)(x − 4)

Answer: 3x2 − 16x + 16

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

Answer: 2x2 − 7x + 6

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

Answer: 9x2 − 24x + 15

  1. 3x × 3x = 9x2
  2. 3x × −3 + −5 × 3x = −9x + −15x = −24x
  3. −5 × −3 = 15
12.Expand and simplify: (3x + 2)(x + 5)

Answer: 3x2 + 17x + 10

  1. 3x × x = 3x2
  2. 3x × 5 + 2 × x = 15x + 2x = 17x
  3. 2 × 5 = 10
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