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MathidiaMathematics Academy
Expressions and equations
Lesson 38 of 75
Standard practice

Expand a single bracket

Objective. Apply the distributive law to expand expressions.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Expanding a single bracket means multiplying every term inside the bracket by the term directly outside it, using the distributive law. For example, 3(x+4) expands to 3×x+3×4, giving 3x+12. When the term outside is negative, such as −2(x−5), every term inside changes sign appropriately, giving −2x+10. After expanding, any like terms outside the bracket should be collected to finish simplifying. Checking the expansion by substituting a number, such as x=2, into both the bracketed and expanded forms confirms the result is correct.

Worked example

Expand the single bracket in the expression 5(2x − 3) and simplify.

5 … 2
Illustrated card showing 5 … 2
  1. 1Multiply the first term inside by 5: 5×2x=10x.
  2. 2Multiply the second term inside by 5: 5×(−3)=−15.
  3. 3Combine the two results: 10x−15.
  4. 4Check with x=1: bracket gives 5(2−3)=−5, expansion gives 10−15=−5.

Answer: 10x − 15

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Practice

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Common mistake. Pupils often multiply only the first term inside the bracket, turning 4(x+3) into 4x+3 instead of 4x+12. Always multiply every single term inside the bracket by the outside term.

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