1
Identity or equation?
Recognise statements true for all allowed values versus statements true for specific values.
Chapter route
Exploring Algebraic Identities
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Ordered curriculum items
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2
Check an identity
Test an identity with multiple values before proving or using it.
3
Expand (a ± b)^2
Use standard square identities to expand expressions.
4
Use difference of squares
Apply (a + b)(a - b) to simplify products.
5
Expand binomial products
Select a suitable identity to expand binomial expressions efficiently.
6
See identities as areas
Connect algebraic identities with rectangles and squares.
7
Visualise a² - b²
Use area rearrangement to understand the difference of squares.
8
Take out common factors
Identify and remove common algebraic factors.
9
Factor a² - b² forms
Recognise and factor expressions of the form A² - B².
10
Factor perfect squares
Recognise trinomials matching square identities.
11
Split and factor quadratics
Use product-sum reasoning to factor quadratic expressions.
12
Use tiles to factor
Represent quadratic expressions using algebra tiles and identify factors.
13
Factor without tiles
Move from visual models to symbolic factorisation.
14
Build a new identity
Substitute expressions into known identities to create related identities.
15
Calculate quickly with identities
Apply algebraic identities to compute numerical products and squares efficiently.
16
Find forbidden values
Determine values that make denominators zero.
17
Simplify rational expressions
Factor numerator and denominator and cancel common non-zero factors.
18
Check cancellations
Avoid invalid cancellation and justify each simplification step.
19
Simplify step by step
Break multi-step simplification into expansion, factorisation and cancellation stages.
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