Quadratics — NSW Year 10 Core Maths
Expanding binomial products and factorising expressions, including grouping in pairs. Two subtopics and 40 practice questions, each with a worked solution, aligned to NESA MA5-ALG-C-01 and MA5-ALG-P-01.
Quadratics in NSW Year 10 Core
A quadratic expression has a squared term, such as \(x^2 - 2x - 24\). In Year 10 Core, students expand pairs of brackets, including perfect squares and differences of two squares, and factorise by taking out common factors and by grouping in pairs. Factorising trinomials and solving quadratic equations are studied in Year 10 Advanced.
The two subtopics below build in that order: expanding, then factorising. Quadratics is one of the 11 topics in NSW Year 10 Maths Core and sits within NESA's Number and Algebra strand (NESA outcomes MA5‑ALG‑C‑01, MA5‑ALG‑P‑01 and MA5‑ALG‑P‑02). Expanding and factorising lead on to graphing parabolas.
Subtopics
Quadratics: common questions
What is a difference of two squares?
It is what you get when you expand \((a + b)(a - b)\): the middle terms cancel, leaving \(a^2 - b^2\). For example, \((x + 5)(x - 5) = x^2 - 25\).
How do you expand a binomial product?
Multiply each term in the first bracket by each term in the second, then collect like terms: \((p + 4)(p - 7) = p^2 - 7p + 4p - 28 = p^2 - 3p - 28\).
How do you factorise by grouping in pairs?
Split the four terms into two pairs, take out a common factor from each pair, then take out the common bracket: \(ax + ay + 3x + 3y = a(x + y) + 3(x + y) = (x + y)(a + 3)\).
Which NESA outcomes cover quadratics in Year 10 Core?
Expanding binomial products comes under MA5‑ALG‑C‑01, and factorising belongs to the Path outcomes MA5‑ALG‑P‑01 and MA5‑ALG‑P‑02.
Why learn to expand and factorise?
Expanding and factorising are used to simplify algebraic fractions and to work with parabolas, and they are needed throughout Stage 6 maths.