Algebraic Expressions and Identities

intermediate24 min read

The standard square and cube identities, and how to use them to expand, factorise and evaluate expressions quickly from summary values like a+b and ab.

What you will be able to do

State and apply the square identities for (a+b)^2, (a-b)^2, a^2-b^2 and (a+b+c)^2.
State and apply the cube identities for (a+b)^3, (a-b)^3, a^3+b^3 and a^3-b^3.
Evaluate a^2+b^2 and a^3+b^3 from a+b and ab without finding a and b.
Use a^2-b^2 = (a+b)(a-b) to simplify awkward products at speed.

What is inside this lesson

1Why identities matter
2Terms, coefficients and degree
3The square identities
4The cube identities
5Evaluating from a+b and ab
6Worked examples
7Common mistakes
8Quick revision
9Practice

The lesson itself is for members

Reading the 9 sections above, the worked examples and the practice set is free — the whole knowledge base is on the free plan, along with flashcards, private notes and Ask Onely.

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