Algebra: Expanding and Factorising — NSW Year 9 Core Maths
Algebraic fractions, expanding, factorising and binomial products. Five subtopics and 100 practice questions, each with a fully worked solution, aligned to NESA outcomes MA5-ALG-C-01 and MA4-ALG-C-01.
Algebra: Expanding and Factorising in NSW Year 9
This topic builds the algebra skills that the rest of Year 9 relies on. Students simplify algebraic fractions such as \(\frac{3x}{4} \times \frac{2x}{9}\) and \(\frac{x}{2} + \frac{x}{3}\), expand brackets with negative terms, factorise by taking out the highest common factor, and multiply two brackets together, as in \((x + 7)(x - 2) = x^2 + 5x - 14\).
The five subtopics below start with multiplying, dividing, adding and subtracting algebraic fractions, then move to expanding and simplifying, factorising, and expanding binomial products. Algebra: Expanding and Factorising is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Number and Algebra strand. The fractions and expanding work is Stage 5 Core content under NESA outcome MA5‑ALG‑C‑01, and factorising by a common factor extends the Stage 4 outcome MA4‑ALG‑C‑01. These skills lead straight into equations, and into factorising quadratic expressions for students who go on to Advanced maths.
Subtopics
Algebra: Expanding and Factorising: common questions
How do you multiply algebraic fractions?
Multiply the numerators and multiply the denominators, cancelling any common factors first. For example, \(\frac{3x}{4} \times \frac{2x}{9} = \frac{6x^2}{36} = \frac{x^2}{6}\).
How do you add algebraic fractions with different denominators?
Rewrite both fractions over a common denominator, then add the numerators. For \(\frac{2x}{3} + \frac{x}{5}\), use \(15\): \(\frac{10x}{15} + \frac{3x}{15} = \frac{13x}{15}\).
What is the difference between expanding and factorising?
Expanding removes brackets, so \(4(x - 2)\) becomes \(4x - 8\). Factorising does the reverse, taking out the highest common factor, so \(4x - 8\) becomes \(4(x - 2)\). You can always check a factorisation by expanding it again.
How do you expand two brackets?
Multiply each term in the first bracket by each term in the second, then collect like terms. For example, \((x + 7)(x - 2) = x^2 - 2x + 7x - 14 = x^2 + 5x - 14\).
Which NESA outcomes cover expanding and factorising in Year 9?
Algebraic fractions with number denominators, expanding brackets and binomial products are Stage 5 Core content under MA5‑ALG‑C‑01. Factorising by taking out a common factor comes from the Stage 4 outcome MA4‑ALG‑C‑01, revised and extended in Year 9.