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

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

1.Expand and simplify: (2x − 4)(3x − 7)

Answer: 6x2 − 26x + 28

  1. 2x × 3x = 6x2
  2. 2x × −7 + −4 × 3x = −14x + −12x = −26x
  3. −4 × −7 = 28
2.Expand and simplify: (2x − 5)(2x − 1)

Answer: 4x2 − 12x + 5

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

Answer: 2x2 − 8x + 6

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

Answer: 4x2 − 18x + 14

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

Answer: 8x2 + 6x − 14

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

Answer: 2x2 + 5x − 12

  1. 2x × x = 2x2
  2. 2x × 4 + −3 × x = 8x + −3x = 5x
  3. −3 × 4 = −12
7.Expand and simplify: (4x + 3)(2x + 4)

Answer: 8x2 + 22x + 12

  1. 4x × 2x = 8x2
  2. 4x × 4 + 3 × 2x = 16x + 6x = 22x
  3. 3 × 4 = 12
8.Expand and simplify: (2x + 7)(2x + 7)

Answer: 4x2 + 28x + 49

  1. 2x × 2x = 4x2
  2. 2x × 7 + 7 × 2x = 14x + 14x = 28x
  3. 7 × 7 = 49
9.Expand and simplify: (2x + 6)(x − 2)

Answer: 2x2 + 2x − 12

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

Answer: 3x2 − 10x − 25

  1. 3x × x = 3x2
  2. 3x × −5 + 5 × x = −15x + 5x = −10x
  3. 5 × −5 = −25
11.Expand and simplify: (2x − 3)(3x + 5)

Answer: 6x2 + x − 15

  1. 2x × 3x = 6x2
  2. 2x × 5 + −3 × 3x = 10x + −9x = x
  3. −3 × 5 = −15
12.Expand and simplify: (4x + 6)(2x + 5)

Answer: 8x2 + 32x + 30

  1. 4x × 2x = 8x2
  2. 4x × 5 + 6 × 2x = 20x + 12x = 32x
  3. 6 × 5 = 30
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