Algebra: Expanding and Factorising — NSW Year 9 Advanced Maths
Algebraic fractions, expanding brackets and every main factorising method. Nine subtopics and 180 practice questions with fully worked solutions, aligned to NESA outcomes MA5-ALG-C-01, MA5-ALG-P-01 and MA5-ALG-P-02.
Algebra: Expanding and Factorising in NSW Year 9 Advanced
Expanding and factorising are opposite processes: expanding removes brackets and factorising puts them back. In Year 9 Advanced, students work with algebraic fractions, expand binomial products, and factorise using common factors, grouping in pairs, the difference of two squares, perfect squares and quadratic trinomials, then use factorising to simplify algebraic fractions.
The nine subtopics below start with operations on algebraic fractions, move through expanding brackets and binomial products, then cover simple factorising, special binomial products, quadratic expressions and mixed factorisations, and finish with factorising algebraic fractions. Algebra: Expanding and Factorising is one of the 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Number and Algebra strand (NESA outcomes MA5‑ALG‑C‑01, MA5‑ALG‑P‑01 and MA5‑ALG‑P‑02). These skills are needed to solve quadratic equations and graph parabolas.
Subtopics
Algebra: Expanding and Factorising: common questions
What is the difference between expanding and factorising?
Expanding multiplies out brackets, as in \(3x(2x - 5) = 6x^2 - 15x\). Factorising reverses this, writing the expression as a product: \(6x^2 - 15x = 3x(2x - 5)\). Expanding a factorised answer is a quick check.
How do you factorise a quadratic trinomial?
For \(x^2 + bx + c\), find two numbers that multiply to \(c\) and add to \(b\). For \(x^2 - x - 6\) the numbers are \(-3\) and \(2\), so \(x^2 - x - 6 = (x - 3)(x + 2)\).
What is the difference of two squares?
It is the pattern \(a^2 - b^2 = (a - b)(a + b)\). For example, \(4x^2 - 9 = (2x - 3)(2x + 3)\), and \(73^2 - 27^2 = 46 \times 100 = 4600\) without a calculator.
How do you simplify an algebraic fraction?
Factorise the numerator and the denominator, then cancel common factors. Only whole factors cancel, never single terms. For example, \(\frac{x^2 - x - 6}{x + 2} = \frac{(x - 3)(x + 2)}{x + 2} = x - 3\).
Which NESA outcomes cover this topic?
Simplifying fractions over number denominators, and expanding, are the Stage 5 Core outcome MA5‑ALG‑C‑01. Pronumeral denominators, common factors and monic quadratics are MA5‑ALG‑P‑01, and special products, non-monic quadratics and grouping are MA5‑ALG‑P‑02.