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The distributive property

Multiply every term inside parentheses by the outside factor.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Factor and constant

The outside factor and inside constant use this range; the outside factor cannot be zero.

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The distributive propertyThe distributive property. Practice. Expand and simplify: 3(x − 2). Expand and simplify: −3(x + 0). Expand and simplify: 2(x + 1). Expand and simplify: 5(x + 2). Expand and simplify: −3(x − 5). Expand and simplify: −5(x + 6). Expand and simplify: 1(x + 7). Expand and simplify: 1(x − 3). Expand and simplify: 3(x − 1). Expand and simplify: −5(x − 4). Expand and simplify: −8(x + 2). Expand and simplify: 8(x − 6).Name __________________________Date _______________The distributive propertyExpand and simplify each expression.Worked exampleExpand −3(x + 4). → −3x − 12Multiply x by −3 to get −3x.1.Expand and simplify: 3(x − 2).2.Expand and simplify: −3(x + 0).3.Expand and simplify: 2(x + 1).4.Expand and simplify: 5(x + 2).5.Expand and simplify: −3(x − 5).6.Expand and simplify: −5(x + 6).7.Expand and simplify: 1(x + 7).8.Expand and simplify: 1(x − 3).9.Expand and simplify: 3(x − 1).10.Expand and simplify: −5(x − 4).11.Expand and simplify: −8(x + 2).12.Expand and simplify: 8(x − 6).MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 24d57599
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Practice + answer key · 2 pages

Algebra

What you’ll practice

Expand a(x + b) into an equivalent linear expression.

The outside factor applies to everything inside the parentheses. Multiply it by x and by the constant, keeping track of negative signs.

How this skill works

Use a(x + b) = ax + ab.

If the outside factor is negative, it changes the sign of both products.

Worked example

Expand −3(x + 4).
  1. Multiply x by −3 to get −3x.
  2. Multiply 4 by −3 to get −12.
  3. Combine the products: −3x − 12.

Answer: −3x − 12

Teaching notes

  • Check that you multiplied the constant as well as x.
Practice questions
  1. Expand and simplify: 3(x − 2).
  2. Expand and simplify: −3(x + 0).
  3. Expand and simplify: 2(x + 1).
  4. Expand and simplify: 5(x + 2).
  5. Expand and simplify: −3(x − 5).
  6. Expand and simplify: −5(x + 6).
  7. Expand and simplify: 1(x + 7).
  8. Expand and simplify: 1(x − 3).
  9. Expand and simplify: 3(x − 1).
  10. Expand and simplify: −5(x − 4).
  11. Expand and simplify: −8(x + 2).
  12. Expand and simplify: 8(x − 6).
Answers and steps
  1. 3x − 6
    1. Multiply both terms inside the bracket by 3: 3x + (3 × −2).
    2. The result is 3x − 6.
  2. −3x
    1. Multiply both terms inside the bracket by −3: −3x + (−3 × 0).
    2. The result is −3x.
  3. 2x + 2
    1. Multiply both terms inside the bracket by 2: 2x + (2 × 1).
    2. The result is 2x + 2.
  4. 5x + 10
    1. Multiply both terms inside the bracket by 5: 5x + (5 × 2).
    2. The result is 5x + 10.
  5. −3x + 15
    1. Multiply both terms inside the bracket by −3: −3x + (−3 × −5).
    2. The result is −3x + 15.
  6. −5x − 30
    1. Multiply both terms inside the bracket by −5: −5x + (−5 × 6).
    2. The result is −5x − 30.
  7. x + 7
    1. Multiply both terms inside the bracket by 1: 1x + (1 × 7).
    2. The result is x + 7.
  8. x − 3
    1. Multiply both terms inside the bracket by 1: 1x + (1 × −3).
    2. The result is x − 3.
  9. 3x − 3
    1. Multiply both terms inside the bracket by 3: 3x + (3 × −1).
    2. The result is 3x − 3.
  10. −5x + 20
    1. Multiply both terms inside the bracket by −5: −5x + (−5 × −4).
    2. The result is −5x + 20.
  11. −8x − 16
    1. Multiply both terms inside the bracket by −8: −8x + (−8 × 2).
    2. The result is −8x − 16.
  12. 8x − 48
    1. Multiply both terms inside the bracket by 8: 8x + (8 × −6).
    2. The result is 8x − 48.