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Simplify

Afrikaans: Vereenvoudig

Express the given expression in its simplest algebraic form. You are not solving for a variable, there is no '= 0' to introduce and no value to find. The goal is to rewrite the expression in fewer or simpler terms: cancel common factors, expand brackets where needed, and collect like terms. The answer is still an expression, not a specific number.

Common mistake

The most common error is setting the expression equal to zero and solving for x, as if the question had asked 'solve'. This earns no marks because you've answered a completely different question. A related mistake is simplifying partway and then stopping, 'simplify fully' means reaching the simplest form with no further factorisation or cancellation possible. Check: can you cancel anything else? If yes, you are not finished.

Signal phrases

These are the words that tell you this instruction is being used.

  • Simplify fully
  • Write in simplest form
  • Simplify, without using a calculator
  • Simplify the expression

Past paper examples

Simplify fully: (x² − 9) / (x² + x − 6)

Source: DBE Mathematics Paper 1, November 2021, Question 1.3

Simplify: 3x²y / (6xy²) without using a calculator.

Source: DBE Mathematics Paper 1, May/June 2023, Question 1.1

Test yourself

Before you read the answer, what is this question asking you to do?

Simplify fully: (x² + 3x) / (x² + x − 6)

Practice question: not from a past paper

Where this comes up