Factorising is putting an expression into brackets to make it look more simple and easier to understand. For example putting 2x² + x - 3 into the form (2x + 3)(x - 1). This is an important way of solving quadratic equations. The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1).
Expanding brackets is the opposite of factorising, so instead of putting an expression into brackets, we work out an expression from the brackets.
For an expression of the form a(b + c), the expanded version is ab + ac. You multiply the term outside the bracket by everything inside the bracket: