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MathidiaMathematics Academy
Algebraic manipulation
Lesson 17 of 75
Easy practice

Expand brackets

Objective. Expand single brackets including negative coefficients.

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

Learn: the key idea

Expanding brackets means multiplying every term inside the bracket by the term outside, removing the bracket to leave a simplified expression. For a single bracket like 3(2x − 5), multiply both 2x and −5 by 3 to get 6x − 15. When the term outside is negative, such as −2(x − 4), take care with signs: multiplying −2 by −4 gives +8, so the result is −2x + 8. Always check the number of terms inside the bracket matches the number of terms in the expanded answer, and recombine any like terms afterwards.

Worked example

Expand the brackets in the expression −3(2x − 5).

3 … 2
Illustrated card showing 3 … 2
  1. 1Multiply the outside term by the first term: −3 × 2x = −6x
  2. 2Multiply the outside term by the second term: −3 × (−5) = 15
  3. 3Combine the two results: −6x + 15
  4. 4Check by substituting x = 1: −3(2 − 5) = −3 × (−3) = 9, and −6 + 15 = 9

Answer: −6x + 15

Concept mastery

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Practice

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Common mistake. Pupils often forget to multiply the second term inside the bracket, expanding 4(x + 3) as 4x + 3 instead of correctly multiplying both terms to get 4x + 12.

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