GCSE Maths: Algebra Revision Guide

Expanding brackets

To expand a single bracket, multiply everything inside it by the term outside: 3(x + 4) = 3x + 12. For two brackets, multiply every term in the first bracket by every term in the second (sometimes called FOIL — First, Outer, Inner, Last): (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.

Factorising

Factorising is the reverse of expanding. First look for a common factor: 4x + 12 = 4(x + 3). For a quadratic like x² + 7x + 10, find two numbers that multiply to give the last number (10) and add to give the middle number (7) — here, 2 and 5, so it factorises to (x + 2)(x + 5).

Solving linear equations

Keep the equation balanced — whatever you do to one side, do to the other. To solve 3x + 4 = 19: subtract 4 from both sides to get 3x = 15, then divide both sides by 3 to get x = 5.

Simultaneous equations

When you have two equations with two unknowns, you can eliminate one variable by adding or subtracting the equations, or substitute one equation into the other. Always check your answer works in both original equations.

Common mistakes

• Forgetting to multiply every term inside a bracket, not just the first one.
• Sign errors when moving terms across the equals sign — remember to flip the sign.
• Mixing up factorising and expanding — always check your factorised answer by expanding it back out.