Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
NA6-6
New NZC (2026)
NZC26-P4-ALG-ER-K-Y10-06
Resources
- CorbettMaths on factorising difference between squaresQuestions PDF · Answers
- Beta: Single brackets: Ex 9.04 to Ex 9.07, pgs 171 to 174
Terminology
- difference between two squares
- perfect square
- factorise
- highest common factor (hcf)
- quadratic
- difference of two squares
- coefficient
- constant term
Task goals
- Factorise a perfect-square trinomial with a leading coefficient of 1, such as $x^2+6x+9$, into $(x+a)^2$ form.
- Factorise a difference of two squares with a leading coefficient of 1, such as $x^2-16$, into $(x-a)(x+a)$ form.
- Fill in a missing number in a partially-given perfect-square or difference-of-squares factorisation, such as $x^2+12x+36=(x+\square)^2$ or $p^2-64=(p-\square)(p+\square)$.
- Factorise a perfect-square trinomial or difference of two squares where the leading coefficient is greater than 1, such as $4y^2+12y+9$ or $25p^2-1$.
- Decide whether a given factorisation is correct, or identify which of four expressions does not belong with the others.
- Factorise fully an expression requiring two applications of difference of squares, such as $x^4-81$.
- Explain how to tell whether a quadratic is a perfect-square trinomial or a difference of two squares.
- Given the area of a square as a quadratic expression, find an expression for its side length.
Where this fits
What leads into this objective, and where it goes next.
Before
Solving quadratics
Solving Quadratic Equations by Factorising (Null Factor Law)
Solving Factorised Equations (Null Factor Law)
You are here
Factorising special double brackets (perfect squares, difference between squares)
Know
There are specific factorising relationships that are useful to recognise: x(x + a) = x^2 + ax; difference of two squares: (x + a)(x − a) = x^2 − a^2; square of a sum: (x + a)^2 = x^2 + 2ax + a^2; square of a difference: (x − a)^2 = x^2 − 2ax + a^2.
Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-K-Y10-06
Also under NA6-6:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.