# NCERT Class 9 Mathematics Chapter 4 Exploring Algebraic Identities Solutions: In-Text and Exercise Questions Explained | SwaVid

This document provides questions and step-by-step solutions for Chapter 4, "Exploring Algebraic Identities," from the NCERT Class 9 Mathematics textbook...

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# Exploring Algebraic Identities

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Chapter 4 · Class 9 Mathematics

This document provides questions and step-by-step solutions for Chapter 4, "Exploring Algebraic Identities," from the NCERT Class 9 Mathematics textbook "Ganita Manjari." The questions are transcribed directly from the official NCERT PDF (iemh104.pdf), including in-text activities like "Think and Reflect," "Do This," "Try These," and the end-of-chapter "Exercise 4.1."

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In-text Questions

Answer: One pattern is that the differences between consecutive square numbers form an arithmetic progression with a common difference of 2. Another pattern is that for any four consecutive square numbers, the sum of the first and last minus the sum of the middle two is always 4.

The example in the textbook for 3 consecutive squares showed a result of 2. This question asks to find a pattern for 4 consecutive squares.

Exercise 4.1

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- Let the four consecutive square numbers be (n-1)², n², (n+1)², and (n+2)².
- Consider the differences between consecutive squares:
- n² - (n-1)² = n² - (n² - 2n + 1) = 2n - 1
- (n+1)² - n² = (n² + 2n + 1) - n² = 2n + 1
- (n+2)² - (n+1)² = (n² + 4n + 4) - (n² + 2n + 1) = 2n + 3
- The differences form an arithmetic progression: 2n-1, 2n+1, 2n+3. The common difference is 2.
- Another pattern: Sum of the first and last square numbers minus the sum of the middle two square numbers.
- [(n-1)² + (n+2)²] - [n² + (n+1)²]
- = [n² - 2n + 1 + n² + 4n + 4] - [n² + n² + 2n + 1]
- = [2n² + 2n + 5] - [2n² + 2n + 1]
- = 4
- This pattern shows that for any four consecutive square numbers, the sum of the first and last minus the sum of the middle two is always 4.
- NCERT Class 9 Mathematics textbook: Ganita Manjari : Chapter 4: Exploring Algebraic Identities

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