How to answer "Show that" questions in GCSE Maths

What it means

You are given the final result. Your job is to produce every working step that connects the start (given values or expression) to the end (the stated result). Starting from the answer and working backwards earns zero — the mark scheme awards method, not the final number.

What examiners want

• Start from the given expression or values — never from the stated result
• Every line of working clearly written, with the operation visible
• Reach the stated result exactly as printed (right form, right precision)
• A final line that matches the requested form, even if your intermediate working used a different form

Worked example

Show that (2x + 3)(x − 4) = 2x² − 5x − 12.

Start with the left-hand side. Expand using FOIL: (2x)(x) + (2x)(−4) + (3)(x) + (3)(−4) = 2x² − 8x + 3x − 12. Collect like terms: 2x² − 5x − 12. This matches the right-hand side, so the result is shown.

Common mistakes

• Starting from the answer (e.g. 2x² − 5x − 12) and factorising backwards — this earns zero
• Skipping the like-terms step — examiners want to see −8x + 3x = −5x explicitly
• Writing "= 2x² − 5x − 12" only at the end, with no working before it
• Using approximations or rounded values when the result is exact

Marks tip

Treat every "show that" as a method-marks question. The final line being correct earns at most one mark out of three or four. The rest live in the working.

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