Factorising single brackets

Find the highest common factor of the terms and write the expression as a single bracket.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA5-8
New NZC (2026)
  • NZC26-P4-ALG-ER-P-Y9-01
  • NZC26-P3-ALG-ER-K-Y8-02
  • NZC26-P3-ALG-ER-P-Y8-05

Resources

  • Alpha textbook: Factorising by determining the common factor, Ex
  • Alpha textbook: 15.10, pg 249 and Ex 15.12, pg 250
  • Alpha textbook: Factorising by taking out the highest common factor,
  • Alpha textbook: Ex 15.14, pg 251
  • Alpha textbook: Factorising, Ex 15.13, pg 250 and PSE 15G, pg 250
  • Alpha textbook: Factorising with letters as common factors, Ex 15.16,
  • Alpha textbook: pg 252
  • Alpha textbook: Check Your Understanding to review EXPANDING and
  • Alpha textbook: FACTORISING, pg 253
  • CorbettMaths on factorising single bracketsQuestions PDF · Answers
  • Beta: Single brackets: Ex 9.04 to Ex 9.07, pgs 171 to 174

Terminology

  • single bracket
  • factorise
  • factor
  • term
  • coefficient
  • common factor
  • highest common factor (HCF)
  • divide

Task goals

  • Find the highest common factor of algebraic terms and factor it out to write expressions in the form $a(bx+c)$.
  • Use division to extract the common factor, then check by expanding back to the original form.
  • Apply factorising to expressions with letter factors, negative terms, and multiple terms inside the bracket.

Where this fits

What leads into this objective, and where it goes next.

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Factorising single brackets

Factorising single brackets

Do

Simplifying and manipulating algebraic expressions involving sums, products, differences, and positive integer powers, by: collecting like terms; factorising using common factors; expanding products, including multiplying a single term by a bracketed term.

Statement▸
Year 9 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y9-01

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