Algebraic Identities

What this lesson covers

Algebraic Identities is a 10-part Class 8 Mathematics lesson. Each part makes one point and then hands over to the next, so it can be read in a sitting or picked up again at the part you stopped on. It defines the idea in plain words before using it, works through an example step by step, breaks the topic into its parts and compares them, shows where it is used outside the textbook, names the mistakes that cost marks in an exam, ends with a recap of what to remember.

How it begins

An equation is true for particular values. x + 3 = 7 is true only when x = 4. An identity is true for every value. (a + b)² = a² + 2ab + b²Substitute any numbers you like and it holds. Why they are worth memorising: they let you expand and factorise instantly, and factorising is what makes quadratic equations solvable next year.

The 10 parts

1. An identity is always true
2. The three standard identities
3. Why (a+b)² is not a² + b²
4. Using identities for mental arithmetic
5. Factorising with the identities
6. Recognising the pattern under disguise
7. Why identities matter later
8. Where it usually goes wrong
9. What to remember
10. Watch one worked through