Linear Expressions: Expand, Factorise and Simplify — AC9M8A01

• Recognise when linear expressions are equivalent.
• Use named number properties to rewrite expressions.
• Expand and factorise using symbols and area/algebra-tile models.
• Combine like terms and verify a rewrite by substitution.

Recall variables, coefficients, constants, like terms, substitution, integer arithmetic and distributivity in numerical calculations.

An equivalent expression may look different but gives the same value for every permitted substitution. Algebraic manipulation is not arbitrary symbol movement: each step must preserve equivalence.

Distributivity connects factorised and expanded forms: a(b+c)=ab+ac. The same relationship works in reverse when factorising. Like terms combine only when their variable parts match exactly.

The AC9 elaborations use algebra tiles and area models to make these properties visible. Use the model to explain why a rewrite works, then compress the reasoning into symbolic steps.

• Combining unlike terms: 3x+2 is not 5x.
• Distributing to only the first term: 4(x+3)=4x+12, not 4x+3.
• Incorrect factorising: 8x+12=4(2x+3), not 4(x+12).
• Moving terms without justification: name the property or inverse operation and verify.

1. Use an area model to expand 2(x+5).
2. Simplify 7x+4−3x+9 and identify the like terms.
3. Factorise 9y+27.
4. Verify 3(a−2)=3a−6 using a=4.

1. Simplify 5x+7+2x−3.
2. Expand 4(2y−5).
3. Factorise 12a+18.
4. Simplify 3(2m+1)−4m.
5. Explain why 2x+3x=5x but 2x+3x² cannot combine.
6. Find and correct the error in 6(p+4)=6p+4.
7. Create two expressions equivalent to 5x+10 and justify each.

A rectangle has side lengths 2x+3 and 4 units. One student writes the area as 8x+12 and another writes 4(2x+3). Explain why both are correct, then determine whether 2(4x+6) is also equivalent.

1. What does equivalent mean? The expressions have the same value for every permitted value of the variables.
2. Why can expanded and factorised forms both be correct? Distributivity guarantees a(b+c)=ab+ac.
3. When may terms be combined? When their variable parts, including exponents, match.
4. How can you check a rewrite? Substitute convenient values; a counterexample disproves a false equivalence.

1. Simplify 4(2x−3)+5x and justify each transformation.
   Review hint: Expand accurately and combine only like terms.
2. Evaluate the claim 6x+15=3(2x+15) and correct it.
   Review hint: Re-expand the proposal and give the correct factorisation.
3. Create expanded and factorised forms of one linear expression and prove equivalence.
   Review hint: Use distributivity or a representation, not one numerical example.

• I distinguish coefficients, constants and like terms.
• I expand and factorise using distributivity.
• I combine only like terms.
• I can prove or disprove an equivalence claim.

Exit ticket: Why does one substitution help check a rewrite but not replace an algebraic proof?

Australian Curriculum v9.0 — AC9M8A01: create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8A01: Exact relationship.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-ALG-C-01; MAO-WM-01: Exact. MA4-ALG-C-01 directly covers algebraic expressions including expansion and factorisation; MAO-WM-01 supports reasoning and communication.

• AC9M8A02 — linear equations, graphs and inequalities
• AC9M8N04 — rational-number operations

• Australian Curriculum v9.0
• Victorian Curriculum F–10 Version 2.0 Mathematics
• NSW Mathematics K–10 Syllabus (2022)

Curriculum equivalents for Create, expand, factorise, rearrange and simplify linear expressions, applying the...

Mapped skill: create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.