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Algebra · Foundation & Higher

Simplifying expressions

Simplifying algebraic expressions means collecting like terms and applying index laws. Like terms have exactly the same letters and powers and can be added or subtracted.

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Key facts to remember

  • 1Like terms have the same letter(s) and power(s): 3x and 5x are like terms; 3x and 3x² are not.
  • 2Collect like terms by adding or subtracting their coefficients.
  • 3When multiplying terms: multiply coefficients and add indices (e.g. 3x² × 2x³ = 6x⁵).
  • 4When dividing terms: divide coefficients and subtract indices (e.g. 6x⁵ ÷ 2x² = 3x³).
  • 5An expression cannot be simplified further if all remaining terms are unlike.
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Worked examples

Example 1

Simplify 5x² + 3x − 2x² + 4x − 1

Working

  1. Group like terms: (5x² − 2x²) + (3x + 4x) − 1
  2. = 3x² + 7x − 1
Answer3x² + 7x − 1
Example 2

Simplify 4a²b × 3ab³

Working

  1. Multiply coefficients: 4 × 3 = 12
  2. Multiply a terms: a² × a = a³
  3. Multiply b terms: b × b³ = b⁴
  4. = 12a³b⁴
Answer12a³b⁴
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Common mistakes

✗Adding unlike terms (e.g. writing 3x + 2x² = 5x³).
✗Forgetting to carry the negative sign when collecting terms.
✗Adding indices when multiplying coefficients (e.g. 3x² × 2x = 6x² instead of 6x³).
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Exam tips

✓Underline or highlight like terms in different colours before collecting them.
✓With index laws: × means add indices, ÷ means subtract indices, power of a power means multiply indices.

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