Summary
Chapter 6 of Class 8 Maths, "We Distribute, Yet Things Multiply", explores the distributive property of multiplication over addition and uses it to solve multiplication patterns, expand algebraic expressions, and develop fast multiplication techniques for special numbers.
This chapter teaches how to apply the distributive property—a(b + c) = ab + ac—to expand products of multi-term expressions and understand how products change when numbers are incremented or decremented. Students learn three key identities: (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², and (a + b)(a − b) = a² − b². The chapter also shows how the distributive property enables fast multiplication techniques for numbers like 11, 101, and 1001, and demonstrates how multiple algebraic approaches can describe the same pattern.
Key points & formulas
- 01The distributive property: a(b + c) = ab + ac, and its extension (a + m)(b + n) = ab + mb + an + mn
- 02When product ab is increased by 1 on one factor, the product increases by the other factor; when both increase by 1, the increase is a + b + 1
- 03Square of sum identity: (a + b)² = a² + 2ab + b²
- 04Square of difference identity: (a − b)² = a² − 2ab + b²
- 05Difference of squares identity: (a + b)(a − b) = a² − b²
- 06Fast multiplication rules using distributivity: multiply by 11 by adding adjacent digits; multiply by 101 by placing the number 100 places apart and adding the overlap
- 07Algebraic identities can be verified and visualized geometrically using rectangular area decomposition
Frequently asked questions
01What is the distributive property explained in Chapter 6?
The distributive property states that a(b + c) = ab + ac. It allows you to multiply a number by a sum by distributing the multiplication across each term. For example, 23(27 + 1) = 23 × 27 + 23 × 1.
02What are the three key algebraic identities in Class 8 Chapter 6?
The three key identities are: (a + b)² = a² + 2ab + b² (square of sum), (a − b)² = a² − 2ab + b² (square of difference), and (a + b)(a − b) = a² − b² (difference of squares).
03How does the distributive property help with fast multiplication?
You can write numbers in a convenient form. For example, to multiply by 11, write 11 = 10 + 1, then 3874 × 11 = 3874(10 + 1) = 38740 + 3874. Similarly, 101 = 100 + 1 allows multiplication by 101 by shifting and adding digits.
04How do you expand (a + b)(c + d) using the distributive property?
Multiply each term in the first expression by each term in the second: (a + b)(c + d) = ac + ad + bc + bd. This is the generalization that all four products must be added.
05Can I use these identities to find squares of large numbers quickly?
Yes. For example, 46² = (40 + 6)² = 1600 + 480 + 36 = 2116, or 99² = (100 − 1)² = 10000 − 200 + 1 = 9801. Ancient mathematicians like Brahmagupta and Sridharacharya used these methods for fast computation.
More chapters in Ganita Prakash
This is the complete Ganita Prakash Chapter 6 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 8 textbooks.
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