IGCSEMaths Algebra.

Sign errors when expanding brackets

Remember: −3(x − 4) = −3x + 12, not −3x − 12. The negative multiplies every term inside.

Cancelling terms instead of factors in algebraic fractions

You can only cancel common factors, not individual terms. Factorise first, then cancel.

Forgetting the middle term when squaring brackets

(2x + 1)² = 4x² + 4x + 1, not 4x² + 1. Always use FOIL or the identity (a + b)² = a² + 2ab + b².

Using substitution as proof in algebraic proof questions

Testing specific values is verification, not proof. Use algebraic variables (2n for even, 2n + 1 for odd) and show the result holds generally.

Mixing up elimination and substitution methods

Use elimination for two linear equations (match coefficients). Use substitution when one equation is quadratic (rearrange the linear one first).