AC9M9A02 Year 9 Mathematics

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

Elaborations

• • Elaboration 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
• • Elaboration 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
• • Elaboration 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