NSW Syllabuses

# Mathematics K–10 - Stage 5.3 - Number and Algebra Algebraic Techniques §

## Outcomes

#### A student:

• MA5.3-1WM

uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures

• MA5.3-5NA

selects and applies appropriate algebraic techniques to operate with algebraic expressions

## Content

• add and subtract algebraic fractions, including those with binomial numerators,
eg $$\frac{2x+5}{6} + \frac{x-4}{3}$$,  $$\frac{x}{3}-\frac{x+1}{5}$$
• Expand binomial products using a variety of strategies (ACMNA233)
• recognise and apply the special product, $$(a-b)(a+b) = a^2 - b^2$$
• recognise and apply the special products, $$\begin{cases} (a+b)^2 = a^2 + 2ab + b^2 \\ (a-b)^2 = a^2 - 2ab + b^2 \end{cases}$$
• 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 $$(3x + 1) (2 - x) + 2x +4$$, $$(x-y)^2 - (x+y)^2$$
• common factors
• a difference of two squares
• grouping in pairs for four-term expressions
• perfect squares
• quadratic trinomials (monic and non-monic)
• 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.