Outcomes
A student:

 MA5.31WM
uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures

 MA5.35NA
selects and applies appropriate algebraic techniques to operate with algebraic expressions
Content
 Students:
 Add and subtract algebraic fractions with numerical denominators, including those with binomial numerators

add and subtract algebraic fractions, including those with binomial numerators,
eg \( \frac{2x+5}{6} + \frac{x4}{3} \), \( \frac{x}{3}\frac{x+1}{5} \)
 Expand binomial products using a variety of strategies (ACMNA233)
 recognise and apply the special product, \( (ab)(a+b) = a^2  b^2 \)
 recognise and name appropriate expressions as the 'difference of two squares' (Communicating)
 recognise and apply the special products, \( \begin{cases} (a+b)^2 = a^2 + 2ab + b^2 \\ (ab)^2 = a^2  2ab + b^2 \end{cases} \)
 recognise and name appropriate expressions as 'perfect squares' (Communicating)
 use algebraic methods to expand a variety of binomial products, including the special products, eg \( (2y+1)^2 \), \( (3a  1)(3a + 1) \)
 simplify a variety of expressions involving binomial products, eg \( (3x + 1) (2  x) + 2x +4 \), \( (xy)^2  (x+y)^2 \)
 Factorise monic and nonmonic quadratic expressions (ACMNA269)
 factorise algebraic expressions, including those involving:
 common factors
 a difference of two squares
 grouping in pairs for fourterm expressions
 perfect squares
 quadratic trinomials (monic and nonmonic)

use a variety of strategies to factorise algebraic expressions,
eg \( 3d^3  3d \), \( 2a^2 + 12a + 18 \), \( 4x^2 20x + 25 \), \( t^2  3t + st 3s \), \( 2a^2b  6ab  3a + 9 \) 
factorise and simplify complex algebraic expressions involving algebraic fractions,
eg \( \frac{x^2 + 3x + 2}{x + 2} \), \( \frac{4}{x^2 + x}  \frac{3}{x^2  1} \), \( \frac{3m  6}{4} \times \frac{8m}{m^2  2m} \), \( \frac{4}{x^2  9} + \frac{2}{3x + 9} \)
Language
When factorising (or expanding) algebraic expressions, students should be encouraged to describe the given expression (or expansion) using the appropriate terminology (eg 'difference of two squares', 'monic quadratic trinomial') to assist them in learning the concepts and identifying the appropriate process.