How many algebraic identities are there in Class 9?

The NCERT Class 9 syllabus covers 8 standard algebraic identities. These include the squares of binomials, difference of squares, product of binomials with common term, square of trinomial, cubes of binomials, and the sum of cubes identity.

How do I remember all 8 algebraic identities?

Do not memorize them as 8 separate formulas. Understand the connections: Identities 1 to 3 are the basic square identities, 4 is for factorising trinomials, 5 extends squaring to three terms, 6 and 7 extend to cubes, and 8 is the special cube factorisation. Practice using them regularly and they become second nature.

What is the difference between an identity and an equation?

An equation is true only for specific values of the variable (like 2x = 6 is true only when x = 3). An identity is true for ALL values of the variables. Algebraic identities are universal truths that work no matter what numbers you substitute.

Which algebraic identity is most important for exams?

The three most frequently tested identities are $(a + b)^2$, $(a - b)^2$, and $a^2 - b^2$. The special case of Identity 8 (when $a + b + c = 0$, then $a^3 + b^3 + c^3 = 3abc$) is also a favourite in board exams.

Are algebraic identities used in higher classes?

Absolutely. Algebraic identities are foundational for Class 10 polynomials and quadratic equations, Class 11 binomial theorem and complex numbers, and Class 12 calculus. Mastering them in Class 9 makes every subsequent year significantly easier.

Study Guide

All Algebraic Identities for Class 9: Explained Visually with Solved Examples

8 standard identities with visual proofs, pattern recognition tips, and 5 solved examples to make algebra feel effortless.

CBSEICSEIBClass 9

SparkEd Team · Reviewed by Vivek Verma6 March 202612 min read

Identities Are Shortcuts, Not Extra Burden

Many students groan when they hear "algebraic identities." They think it means more formulas to memorize on top of an already overloaded syllabus. But here is the truth: identities exist to make your life easier, not harder.

An algebraic identity is an equation that is true for every possible value of the variable. It is not something you solve. It is something you use as a tool. Think of identities like kitchen appliances. You could chop vegetables with a knife (expand everything the long way), or you could use a food processor (apply an identity and get the answer in seconds).

Once you truly understand these 8 identities, you will solve complex expansion and factorisation problems in a fraction of the time. And unlike formulas that only work in specific situations, identities work every single time because they are universally true.

Identity vs Equation: The Key Difference

2x + 3 = 7

The 8 Standard Identities You Must Know

Here are all 8 identities covered in the Class 9 NCERT syllabus. We will go through each one, explain what it means visually, and show when to use it.

5 Solved Examples Using Different Identities

Example 1: Expand $(3x + 4y)^2$
Using Identity 1: $(3x)^2 + 2(3x)(4y) + (4y)^2 = 9x^2 + 24xy + 16y^2$

Example 2: Factorise $25a^2 - 49b^2$
Using Identity 3: $(5a)^2 - (7b)^2 = (5a + 7b)(5a - 7b)$

Example 3: Evaluate $105 \times 95$ without direct multiplication
Using Identity 3: $(100 + 5)(100 - 5) = 100^2 - 5^2 = 10000 - 25 = 9975$

Example 4: Factorise $x^2 + 9x + 20$
Using Identity 4: Find two numbers with sum 9 and product 20. Those are 4 and 5. So $x^2 + 9x + 20 = (x + 4)(x + 5)$

Example 5: If $a + b + c = 0$ , prove that $a^3 + b^3 + c^3 = 3abc$
Using Identity 8: $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$ . Since $a + b + c = 0$ , the right side becomes $0$ . Therefore $a^3 + b^3 + c^3 = 3abc$ .

Common Mistakes to Avoid

(a + b)^2 = a^2 + b^2

How SparkEd Helps You Master Algebraic Identities

At SparkEd, we teach algebraic identities the visual way. Every identity comes with an intuitive explanation. For $(a + b)^2$ , you see the actual square divided into regions. For $a^2 - b^2$ , you see how a rectangle transforms into the product of sum and difference.

Our practice problems start Easy (direct application of one identity), move to Medium (identifying which identity to use and applying it), and go to Hard (multi step problems combining multiple identities). Each solution is visual and step by step, so you never wonder "how did they get from this step to the next."

If you are stuck, Super Power Help gives you a nudge like "Try rewriting this as a difference of squares" without solving the whole problem. And Spark the Coach, our AI tutor, guides you through the pattern recognition process so you build the skill of choosing the right identity on your own.

Written by the SparkEd Math Team

Trusted by thousands of parents and students. Trusted by parents from Google, Microsoft, Meta, McKinsey and more.

Serving Classes 1 to 10 across CBSE, ICSE, IB MYP and Olympiad.

www.sparkedmaths.com | info@sparkedmaths.com

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