Year 9 Mathematics · AC9M9A02

Algebraic Expressions, Binomial Expansion and Factorisation

Simplifying, expanding and factorising are connected ways of rewriting equivalent algebraic expressions. Year 9 extends these skills to binomial products and monic…

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Learning goalsSay it simply

Simplifying, expanding and factorising are connected ways of rewriting equivalent algebraic expressions. Year 9 extends these skills to binomial products and monic quadratics.

By the end of this lesson, you should be able to:

  • simplify expressions by collecting like terms
  • expand products using the distributive law
  • expand binomial products accurately
  • factorise monic quadratics and verify by re-expansion
Key conceptTeach from the board

Simplifying preserves value

Only like terms combine. 3x²+2x−x² becomes 2x²+2x.

Expansion removes brackets by distribution

Every term in one factor multiplies every term in the other; (x+3)(x+5)=x²+8x+15.

Factorisation reverses expansion

For x²+8x+15, find integers with product 15 and sum 8: 3 and 5, giving (x+3)(x+5).

Verification is built in

Expand a factorised answer. If it does not reproduce the original expression, it is wrong.

Worked examplesWe do

Worked examples

AC9M9A02 - Algebraic Expressions, Binomial Expansion and Factorisation
Example 1

Collect like terms 5x²−3x+2x²+7x=7x²+4x.

Example 2

Expand a binomial (x−4)(x+6)=x²+2x−24.

Example 3

Factorise a monic quadratic x²−x−12=(x−4)(x+3).

Example 4

Common factor first 3x²+12x=3x(x+4).

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M9A02: simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions

Victoria: VC2M9A02 — Level 9 Algebra. The mapping names direct Level 9 content where available and explicitly identifies supporting content where the Victorian structure separates an idea differently.

NSW: Stage 5 Core — Algebra and equations; Path — Further algebra and equations. NSW organises Years 7–10 Mathematics through Stage 5 Core content groups and Paths rather than a one-code-per-Year-9 structure, so this lesson does not force a false one-to-one outcome.

Lesson componentAustralian CurriculumVictoriaNSW
Concept teaching + worked examplesAC9M9A02VC2M9A02 — Level 9 AlgebraStage 5 Core — Algebra and equations; Path — Further algebra and equations
Guided + independent practiceApplies the descriptor through progressively less-scaffolded problemsBuilds the corresponding Level 9 mathematical knowledge and fluencySupports Stage 5 Core/Path application and Working mathematically
Reasoning + assessment + masteryChecks transfer, justification, interpretation and model limitsChecks Level 9 reasoning at the mapped content depthChecks relevant Stage 5 reasoning without claiming a false Year 9 equivalent
Questions and answersWith answers
What makes terms like?
They have the same variables raised to the same powers.
What do I look for in x²+bx+c?
Two numbers that multiply to c and add to b.
How do I check factorisation?
Expand the factors and compare with the original.
Practice and reviewReady for practice
  • (x+4)²=x²+16: The middle term is 8x.
  • Factor pairs only need the correct product: They must also add to the middle coefficient.
  • Unlike terms can be collected: x² and x are different term types.
  • Factorisation changes the value: Correct factorisation is equivalent and can be checked by expansion.
  1. [4 marks] Simplify and expand a multi-part expression containing binomial products.
  2. [5 marks] Factorise three monic quadratics including negative constants, showing factor-pair reasoning.
  3. [6 marks] Use the side lengths x+4 and x−2 to form, expand and interpret an area expression, then solve a related condition.

Review hint: A full-mark response shows the method, keeps units and restrictions visible, interprets the result in context and checks whether the answer is reasonable.

Curriculum alignmentStart here

Simplifying, expanding and factorising are connected ways of rewriting equivalent algebraic expressions. Year 9 extends these skills to binomial products and monic quadratics.

By the end of this lesson, you should be able to:

  • simplify expressions by collecting like terms
  • expand products using the distributive law
  • expand binomial products accurately
  • factorise monic quadratics and verify by re-expansion
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