Class 9 Mathematics Chapter 4 Exploring Algebraic Identities – Revision Notes

A handful of standard identities — for squares, cubes and the difference of squares — turn long algebraic expansions into quick substitutions, and this chapter lists them all with their uses.

Last Updated: September 23, 2026

Standard Identities

• (a+b)² = a²+2ab+b²
• (a−b)² = a²−2ab+b²
• a²−b² = (a+b)(a−b)
• (x+a)(x+b) = x²+(a+b)x+ab
• (a+b)³ = a³+b³+3ab(a+b)
• (a−b)³ = a³−b³−3ab(a−b)
• a³+b³ = (a+b)(a²−ab+b²)
• a³−b³ = (a−b)(a²+ab+b²)

Uses

• Quick expansion (substitute into identity).
• Factorisation (recognise pattern, reverse identity).
• Mental calculation (e.g. 102×98 via difference of squares).

One-Line Summary

Algebraic identities are universally true equations that speed up expansion, factorisation, and even arithmetic by letting you substitute into known patterns instead of multiplying term by term.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

Why are algebraic identities useful, rather than just expanding expressions every time?
Algebraic identities are equations that hold true for all values of the variables involved, so recognising a standard pattern like the square of a binomial lets calculations be done quickly without repeating the full multiplication each time.

What is one commonly used algebraic identity introduced in this chapter?
One key identity is that the square of the sum of two terms a and b equals a squared plus 2ab plus b squared, which is widely used to simplify expressions and solve equations faster.

Written by Satish

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