The Algebraic Identities Exercise 4.2 solutions cover both questions of the second exercise set from the new Ganita Manjari book. This is the full NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities Exercise 4.2, where you read the square identities backwards to factor trinomials and square numbers below a round figure.

  • Questions solved: 2 open-ended questions, with every sub-part worked out.
  • Main skill: factoring a2 + 2ab + b2 = (a+b)2 and squaring with (a-b)2.
  • Chapter link: factoring here leads into the three-variable and cube work ahead.

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.

Table of Contents

  1. What Does Algebraic Identities Exercise 4.2 Cover
  2. Algebraic Identities Exercise 4.2 Question Breakdown
  3. Sample Solved Question from Exercise 4.2
  4. How to Use These Algebraic Identities Exercise 4.2 Solutions
  5. More Algebraic Identities Solutions

What Does Algebraic Identities Exercise 4.2 Cover?

This set reads the square identities from right to left. A perfect-square trinomial matches a2 + 2ab + b2 = (a+b)2, so you take the square root of the first and last terms, then check that the middle term is exactly 2ab. Question 1 asks you to factor six trinomials, and two of them need a common factor taken out first. Question 2 uses (a-b)2 = a2 - 2ab + b2 to square numbers like 79 and 299 in your head. Both jobs rest on the same three-part test, and once you trust that test the factoring becomes a quick reverse jigsaw rather than trial and error.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Algebraic Identities Exercise 4.2 Question Breakdown

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

QuestionWhat it asks
Question 1Factor six perfect-square trinomials, such as 9x2 + 24xy + 16y2; parts (v) and (vi) need a common factor first
Question 2Find 792, 1932, and 2992 using the square-of-a-difference identity

Sample Solved Question from Exercise 4.2

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

Question: Factor 9x2 + 24xy + 16y2 completely.

Step 1. Take the square root of the first term. 9x2 = (3x)2, so a = 3x.

Step 2. Take the square root of the last term. 16y2 = (4y)2, so b = 4y.

Step 3. Check the middle term. 2ab = 2(3x)(4y) = 24xy, which matches the given trinomial.

Final answer. 9x2 + 24xy + 16y2 = (3x + 4y)2.

Quick Tip: Matching the first and last squares is not enough. Always confirm the middle term equals 2ab. If it does not match, the trinomial is not a perfect square.

How to Use These Algebraic Identities Exercise 4.2 Solutions

Try each part on your own first, then open the Collegedunia solution to check every line. The steps name the roots clearly and always verify the middle term, so you learn the safe habit. When a leading coefficient is not a perfect square, the solutions show you to pull out a factor before you factor the bracket.

  • Use the three-part test: first square, last square, and middle term equal to 2ab.
  • Self-check: re-expand your factor to be sure it rebuilds the original.
  • Round up to square: for numbers like 299, write 300 - 1 and use (a-b)2.

More Class 9 Maths Algebraic Identities Solutions

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

PageLink
Full ChapterAlgebraic Identities NCERT Solutions
Exercise 4.1Algebraic Identities Exercise 4.1 Solutions
Exercise 4.2Algebraic Identities Exercise 4.2 Solutions
Exercise 4.3Algebraic Identities Exercise 4.3 Solutions
Exercise 4.4Algebraic Identities Exercise 4.4 Solutions
Exercise 4.5Algebraic Identities Exercise 4.5 Solutions
End of ChapterAlgebraic Identities End-of-Chapter Solutions

Algebraic Identities Exercise 4.2 Solutions FAQs

Ques. How many questions are there in Class 9 Maths Exercise 4.2?

Ans. Exercise 4.2 has 2 questions. Question 1 factors six trinomials, and Question 2 squares three numbers. Collegedunia solves both in full.

Ques. Which identities does Exercise 4.2 use?

Ans. It uses a2 + 2ab + b2 = (a+b)2 to factor and (a-b)2 = a2 - 2ab + b2 to square numbers that sit just below a round figure.

Ques. When do I take out a common factor before factoring?

Ans. When the first coefficient is not a perfect square, like 3 or 95, pull out a number first. Then the bracket collapses to a clean (a+b)2.

Ques. Can I download the Exercise 4.2 solutions PDF?

Ans. Yes. The free PDF is on this page, so you can revise offline before your Class 9 annual exam.