Knowledge organisers

Exploring Algebraic Identities: CBSE Class 9 Maths knowledge organiser

Everything to know about exploring algebraic identities on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Identity: An equality that is true for every value of the variables.
Expansion: Multiplying out brackets to write an expression as a sum of terms.
Factorisation: Writing an expression as a product of factors, the reverse of expanding.

Key formulas

Squares	\((a\pm b)^2=a^2\pm2ab+b^2,\) \((a+b)(a-b)=a^2-b^2\)
Product	\((x+a)(x+b)=x^2+(a+b)x+ab\)
Three terms: \((a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\)
Cubes	\((a\pm b)^3=a^3\pm b^3\pm3ab(a\pm b)\)
Sum/difference of cubes	\(a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)\)

Worked example

If \(a + b = 9\) and \(ab = 14\), find \(a^2 + b^2\).

\(a^2 + b^2 = 81 - 28 = 53\).

Common mistakes

\((a + b)^2 = a^2 + b^2\): the middle term \(2ab\) is missing.
\((2x)^2 = 2x^2\): the whole term is squared, \(4x^2\).
Sign of the middle term in \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\).
In \((a + b - c)^2\), the terms \(2bc\) and \(2ca\) become \(-2bc\) and \(-2ca\).

You should be able to…

Pick the right identity to expand a square, a product or a cube, and use one for quick arithmetic.
Factorise with identities and find values such as a² + b² or a³ − b³ from given sums and products.
Expand, evaluate and factorise in multi-part questions and use identities for areas and volumes.
Chain identities, such as from x − 1/x to x⁴ + 1/x⁴, and set up identity-based models.

The printable sheet

Exploring Algebraic Identities knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Exploring Algebraic Identities knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Sequences and Progressions · Linear Equations in Two Variables · Coordinate Geometry · Introduction to Euclid's Geometry: Axioms and Postulates · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Surface Area and Volume · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers