AC9M9A02

simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions

Elaborations

AC9M9A02_E1 - expanding combinations of binomials such as \((x+7)(x+8),\;(x+7)(x-8),\;(x-7)(x+8),\;(x-7)(x-8)\) to identify expansion and factorisation patterns related to \((x+a)(x+b)\;=\;x^2+(a+b)x+ab\), where \(a\) and \(b\) are integers
AC9M9A02_E2 - using manipulatives such as algebra tiles or area models to expand or factorise algebraic expressions with readily identifiable binomial factors; for example, \((x+1)(x+3)\;=\;x^2+4x+3,\;(x-5)^2\;=\;x^2-10x+25\) or \((x-3)^2+4\;=\;x^2-6x+9+4\;=\;x^2-6x+13\)
AC9M9A02_E3 - recognising the relationship between expansion and factorisation, and using digital tools to systematically explore the factorisation of \(x^2+mx+n\) where \(m\) and \(n\) are integers

Achievement Standard Components

ASMAT903 - Students expand binomial products, and factorise monic quadratic expressions.
ASMAT905 - Students use mathematical modelling to solve problems involving change in financial and other applied contexts, choosing to use linear and quadratic functions.
ASMAT906 - They graph quadratic functions and solve monic quadratic equations with integer roots algebraically.