Algebraic Identities Exercise 4.1 Class 9 Maths NCERT Solutions

The Algebraic Identities Exercise 4.1 solutions cover both questions of the first exercise set from the new Ganita Manjari book. This is the full NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities Exercise 4.1, where you expand squares like (a+b)² and square large numbers in your head.

• Questions solved: 2 open-ended questions, with all sub-parts worked out.
• Main skill: using (a+b)² = a² + 2ab + b² to expand and to square numbers.
• Chapter link: this first tool sets up factoring and cubes in the later 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 4.1 Cover?

This exercise builds one identity, the square of a sum: (a+b)² = a² + 2ab + b². In words, the square of a binomial is the square of the first term, plus twice the product, plus the square of the second term. Question 1 asks you to expand six binomial squares, with numbers, fractions, and decimals as terms. Question 2 uses the same identity to find squares like 64² and 205² without long multiplication. The whole set trains you to read a term as a or b and then fill three slots. Once you trust these slots, you never have to expand a square the long way again.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Algebraic Identities Exercise 4.1 Question Breakdown

The table below shows what each of the two questions asks, so you know the exact skill before you start.

Sample Solved Question from Exercise 4.1

Here is Question 1, part (i), solved step by step so you can see the method used across the set.

Question: Expand (7x + 4y)² using (a+b)² = a² + 2ab + b².

Step 1. Read the two terms. Here a = 7x and b = 4y.

Step 2. Find each slot. a² = (7x)² = 49x², then 2ab = 2(7x)(4y) = 56xy, and b² = (4y)² = 16y².

Step 3. Add the three slots in order.

Final answer. (7x + 4y)² = 49x² + 56xy + 16y².

How to Use These Algebraic Identities Exercise 4.1 Solutions

Try each part on your own first, then open the Collegedunia solution to check every line. The steps here name a and b clearly, so you learn the habit, not just the answer. Both questions in this set are open-ended, so a clean worked model matters more than a single final value. Read the fraction and decimal parts slowly, since those are where most marks slip away.

• Learn the slots: square first term, twice the product, square second term.
• Self-check: multiply one binomial the long way to confirm the middle term.
• Practice squaring: split a number as a round part plus a small part, like 105 = 100 + 5.

More Class 9 Maths Algebraic Identities Solutions

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