Algebraic Expressions and Identities
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
Get Pro for full access. This is section 1 of 9; the rest of the lesson opens with Pro at onelystop.in/upgrade.
Why identities matter
An identity is an equation that holds for every value of its letters. Knowing a handful of them turns a page of expansion into one line.
In bank exams they rarely appear as "expand this". They hide inside other questions: a simplification where 103 squared minus 97 squared collapses to a small product, a question that gives you the sum and the product of two numbers and asks for the sum of their squares, a quadratic where the sum and product of the roots is all you need. Learn the identities as tools you reach for, not as a chapter to be memorised and forgotten.
This topic uses the caret sign to mean "to the power of", so a^2 is a squared and a^3 is a cubed.
Reading the 9 sections above is free. A free account opens the first 2 topics of every subject in full, along with flashcards and private notes.