NCERT Class 8 Maths Chapter 6
We Distribute, Yet Things Multiply
NCERT Class 8 Maths Chapter 6 (Ganita Prakash) explores the distributive law and how it connects multiplication with addition and subtraction. This CBSE chapter demonstrates how distribution is a fundamental algebraic principle that underlies operations in arithmetic and algebra, including simplification of expressions and expansion of brackets. Students understand why mathematical rules work, not just how to apply them.
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Key Terms
- Distributive Law
- The rule that states a × (b + c) = a × b + a × c; multiplication distributes over addition (and subtraction).
- Expansion
- The process of removing brackets by applying the distributive law; e.g., 3(x + 4) = 3x + 12.
- Factorisation
- The reverse of expansion — expressing an expression as a product of its factors; e.g., 3x + 12 = 3(x + 4).
- Common Factor
- A number or expression that divides evenly into two or more numbers/terms; used when factorising by taking the common factor outside brackets.
- Identity
- A mathematical equation that is true for all values of the variable; e.g., (a+b)² = a² + 2ab + b² is an algebraic identity.
- Like Terms
- Terms in an algebraic expression that have the same variable(s) raised to the same powers; only like terms can be added or subtracted.
- Area Model
- A visual representation using rectangles to illustrate multiplication and the distributive property; the area of a rectangle (length × width) can be split into parts.
Frequently Asked Questions
What is the distributive law Class 8 Maths?▾
The distributive law states that multiplying a number by a sum is the same as multiplying by each addend separately and then adding: a(b + c) = ab + ac. For example: 6 × (10 + 3) = 6 × 10 + 6 × 3 = 60 + 18 = 78, which is the same as 6 × 13 = 78. This law is fundamental to algebra and arithmetic.
How does the distributive law help in mental maths Class 8?▾
The distributive law makes mental multiplication easier by breaking numbers into convenient parts. For example: 7 × 98 = 7 × (100 - 2) = 700 - 14 = 686. Or 15 × 12 = 15 × (10 + 2) = 150 + 30 = 180. This technique is used widely in Class 8 NCERT Chapter 6 to develop mental calculation strategies.
What is the difference between expansion and factorisation Class 8?▾
Expansion uses the distributive law to remove brackets: 4(x + 3) → 4x + 12. Factorisation is the reverse — it takes the common factor and puts it outside brackets: 4x + 12 → 4(x + 3). Expansion makes expressions longer; factorisation makes them more compact. Both skills are essential for solving algebraic problems in NCERT Class 8 Maths.
How do you use an area model for multiplication Class 8 Maths?▾
An area model represents multiplication as the area of a rectangle. To multiply (a + b)(c + d), draw a rectangle split into four parts: ac, ad, bc, bd. The total area is the sum: ac + ad + bc + bd. This visual method explains why the distributive law works and connects geometry with algebra — a key idea in NCERT Class 8 Maths Chapter 6.
Why is the distributive law important in algebra Class 8?▾
The distributive law is the foundation of algebra. It is used to: expand algebraic expressions (remove brackets), simplify complex expressions, factorise polynomials, prove algebraic identities like (a+b)² = a²+2ab+b², and solve equations. Without understanding distribution, higher algebra in Classes 9 and 10 becomes very difficult.
What are algebraic identities related to the distributive law Class 8?▾
Key identities from NCERT Class 8: (a+b)² = a²+2ab+b², (a-b)² = a²-2ab+b², (a+b)(a-b) = a²-b². These are all proved using the distributive law. They are used as shortcuts in calculations — for example, 99² = (100-1)² = 10000 - 200 + 1 = 9801 without long multiplication.
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