Download We Distribute, Yet Things Multiply – NCERT Class 8 Maths Chapter 6 PDF from the new NCERT Class 8 Maths book Ganita Prakash (2026-27). Read the chapter online or download the free PDF. Distributivity, a (b + c) = ab + ac, is the one rule the whole chapter rests on. Read as an area picture, an a × (b + c) array splits into an a × b array and an a × c array.
We Distribute, Yet Things Multiply PDF – Chapter 6 of Ganita Prakash (Part I)
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 6 PDF | We Distribute, Yet Things Multiply | View PDF |
| Full book | NCERT Class 8 Maths – Ganita Prakash | View Book |
Read Online
What Is in We Distribute, Yet Things Multiply? (Class 8 Maths Chapter 6)
- Distributivity, a (b + c) = ab + ac, is the one rule the whole chapter rests on. Read as an area picture, an a × (b + c) array splits into an a × b array and an a × c array.
- Applying it twice gives Identity 1: (a + m)(b + n) = ab + mb + an + mn — every term of the first bracket times every term of the second. Because the rules of integer multiplication handle the signs, the same identity also covers decreases: just take m or n negative.
- Three special cases are named in the chapter — 1A: (a + b)² = a² + 2ab + b², 1B: (a – b)² = a² + b² – 2ab, 1C: (a + b)(a – b) = a² – b². Each is proved twice: by expanding, and by cutting up a square.
- The same identities give fast mental arithmetic: 65² from 60² and 5², 397 × 403 from 400² – 3², and Sridharacharya’s trick a² = (a + b)(a – b) + b².
- Section 6.3 asks you to find mistakes rather than avoid them; Section 6.4 shows that four different-looking expressions for one dot pattern all simplify to k² + 2k.
- Two algebraic expressions are called an identity when they take the same value for every replacement of the letter-numbers — that is why expanding both sides settles a conjecture for good.
Quick revision – We Distribute, Yet Things Multiply
| Name | Identity | Worked example | Where the chapter uses it |
|---|---|---|---|
| Distributivity | A (b + c) = ab + ac | 23 (27 + 1) = 23 × 27 + 23 | Increase in a product when one factor grows |
| Right form | (a + b) c = ac + bc | (20 + 3) × 7 = 140 + 21 = 161 | Brahmagupta’s khaṇḍa-guṇanam |
| Identity 1 | (a + m)(b + n) = ab + mb + an + mn | (a + 1)(b + 1) = ab + a + b + 1 | Any increase or decrease in both factors |
| Identity 1 with n negative | (a + u)(b – v) = ab + ub – av – uv | (a + 1)(b – 1) = ab + b – a – 1 | One factor up, the other down |
| Identity 1A | (a + b)² = a² + 2ab + b² | 65² = 3600 + 600 + 25 = 4225 | Square of a sum; 104², 46² |
| Identity 1B | (a – b)² = a² + b² – 2ab | 55² = 3600 + 25 – 600 = 3025 | Square of a difference; 99², 91² |
| Identity 1C | (a + b)(a – b) = a² – b² | 397 × 403 = 400² – 3² = 159991 | Pattern 2; 45 × 55; 98 × 102 |
| Sum of two squares | 2(a² + b²) = (a + b)² + (a – b)² | 2(5² + 6²) = 11² + 1² | Pattern 1 |
| Sridharacharya | A² = (a + b)(a – b) + b² | 31² = 32 × 30 + 1 = 961 | Fast squaring |
| Multiply by 11 | N × 11 = N × 10 + N | 495 × 11 = 4|13|14|5 = 5445 | Add neighbouring digits |
| Multiply by 101 | N × 101 = N × 100 + N | 89 × 101 = 8989 | Add digits two places apart |
| Multiply by 99, 999 | N × 99 = N × 100 – N | 9734 × 99 = 973400 – 9734 = 963666 | Same rule, subtraction form |
Old NCERT vs New – Class 8 Maths
This chapter is from Ganita Prakash, the new NCERT Class 8 Maths book (NCF-SE 2023, used from 2025-26). It replaced the old book “Mathematics”, so chapter numbers and names differ from older PDFs.
Solutions and All Chapters
Answers to the exercises and the full chapter list of Ganita Prakash:
We Distribute, Yet Things Multiply – Overview
| Class | Class 8 |
| Subject | Maths |
| Book | Ganita Prakash – new NCERT book |
| Part | Part I |
| Chapter | 6 of 14 – We Distribute, Yet Things Multiply |
| Book pages | 136 – 158 |
| Edition | NCERT Reprint 2026-27 |
| Session | 2026-27 |
| Free – read online or download |
Class 8 Maths Chapter 6 – FAQs
Where can I download We Distribute, Yet Things Multiply Class 8 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 8 Maths Chapter 6 about?
Distributivity, a (b + c) = ab + ac, is the one rule the whole chapter rests on. Read as an area picture, an a × (b + c) array splits into an a × b array and an a × c array.
Is We Distribute, Yet Things Multiply from the new NCERT Class 8 Maths book?
Yes. It is chapter 6 of ganita prakash (part i), the new NCERT Class 8 Maths book for 2026-27.
Is this the latest NCERT edition for 2026-27?
Yes – the PDF is NCERT’s latest edition for the 2026-27 session.
Where are the NCERT Solutions for Class 8 Maths Chapter 6?
Open the NCERT Solutions link above for answers to the exercise questions.