Factorising Expressions

Factorising is the reverse of expanding: it writes an expression as its highest common factor (HCF) times a bracket. In NSW Year 8 maths the HCF can include numbers and pronumerals, so \(15xy - 25x = 5x(3y - 5)\) (NESA outcome MA4‑ALG‑C‑01).

You will find the HCF of two or three terms with powers, such as \(12x^3y - 4xy^2\), and factorise fully so that nothing more can come out. You will check answers by expanding or by substituting values, and take out a whole bracket as the common factor in \(x(y - 3) + 2(y - 3)\). Factorising an area to find the length of a rectangle is one practical use. It is part of Year 8 Algebra.