Algebra – Equations & Inequalities

Expanding means removing brackets by multiplying. Factorising is the reverse — putting an expression back into brackets.

For a single bracket, multiply each term inside by the term outside:
3(2𝑥 + 5) = 6𝑥 + 15

For double brackets, use FOIL — First, Outer, Inner, Last:
(𝑥 + 3)(𝑥 − 2) = 𝑥² − 2𝑥 + 3𝑥 − 6 = 𝑥² + 𝑥 − 6

When factorising a quadratic like 𝑥² + 5𝑥 + 6, you're looking for two numbers that multiply to give +6 and add to give +5. Those numbers are +2 and +3, so it factorises to (𝑥 + 2)(𝑥 + 3).

The difference of two squares is a special pattern:
a² − b² = (a + b)(a − b)

For example: 𝑥² − 25 = (𝑥 + 5)(𝑥 − 5).