Algebraic Identities Exercise 4.3 Class 9 Maths NCERT Solutions

The Algebraic Identities Exercise 4.3 solutions cover all four questions of the third exercise set from the new Ganita Manjari book. This is the full NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities Exercise 4.3, where the square identity grows a third term and you learn to test whether a claim is a true identity.

• Questions solved: 4 open-ended questions, with every sub-part worked out.
• Main skill: using (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca.
• Chapter link: the sign-tracking here prepares you for cube and factoring sets.

These solutions are prepared by subject teachers, matched to the current 2026-27 NCERT, and checked step by step so a Class 9 student can follow each line.

What Does Algebraic Identities Exercise 4.3 Cover?

This set adds a third term to the square identity: (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca. You square numbers mentally, factor three-square trinomials, expand trinomial squares, and check a claimed identity by full expansion. The key new habit is reading the sign of each cross term to fix the sign of each root. This is also the first set where you meet a proof-style question, where one counterexample is enough to show a claim is false.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Algebraic Identities Exercise 4.3 Question Breakdown

The table below shows what each of the four questions asks, so you can plan your practice.

Sample Solved Question from Exercise 4.3

Here is Question 3, part (i), solved step by step so you can see the method used across the set.

Question: Expand (p + 3q + 7r)² using (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca.

Step 1. Name the three terms. Here a = p, b = 3q, and c = 7r.

Step 2. Write the three squares. a² = p², b² = 9q², and c² = 49r².

Step 3. Write the three double-products. 2ab = 6pq, 2bc = 42qr, and 2ca = 14pr.

Final answer. (p + 3q + 7r)² = p² + 9q² + 49r² + 6pq + 42qr + 14pr.

How to Use These Algebraic Identities Exercise 4.3 Solutions

Try each part on your own first, then open the Collegedunia solution to check every line. The steps fill six slots in order, three squares and three double-products, so nothing is missed. For the factoring parts, the solutions read the roots from the squared terms and fix each sign from the cross terms. For Question 4, they show why one counterexample settles the whole claim.

• Fill six slots: three squares plus three double-products 2ab, 2bc, 2ca.
• Track signs: a negative cross term means those two roots have opposite signs.
• Disprove fast: one set of numbers that breaks an equation proves it is not an identity.

More Class 9 Maths Algebraic Identities Solutions

Use the table below to open the full chapter page or any other exercise of this chapter.