Curriculum
GRADE VIII MATHS
Chapters
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Square And Cube
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Power Play
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Story Of Numbers
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Quadrilaterals
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Number Play
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Distribute Mutiply
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Proportional Reasoning 1
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Fraction In Disguise
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Baudhayana-Pythagoras
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Proportional Reasoning 2
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Geometric Themes
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Dots And Lines
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Algebra Play
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Area
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Distribute Mutiply
School Revise · Grade 8 · Maths · Chapter 6 · Ganita Prakash
We Distribute, Yet Things Multiply
Maths, Class 8, Ganita Prakash. The distributive law is the engine behind multiplying algebra. This chapter uses it to multiply expressions and to build the standard identities that expand brackets in one line.
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What this chapter is about
Why does multiplying two brackets give four terms? In this chapter we use the distributive law to multiply algebraic expressions, and see how it produces the standard identities for a perfect square and a difference of two squares.
1. The distributive law
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The distributive law the distributive law says a(b + c) = ab + ac: the outside term multiplies every term inside the bracket To multiply two brackets, each term in the first multiplies each term in the second, then like terms are collected. This is just the distributive law used twice. In real life: Buying 3 packs each holding a pens and b pencils gives 3a pens and 3b pencils, that is 3(a + b) = 3a + 3b. |
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Worked example 1 Question. Expand 4(x + 5).
Answer: 4(x + 5) = 4x + 20. |
2. The standard identities
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The standard identities (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²; (a + b)(a − b) = a² − b² Each identity comes straight from the distributive law: multiply the brackets out and collect like terms. The area model shows the first identity as a square of side (a + b) split into a², two ab rectangles and b². In real life: To find 21² quickly, write it as (20 + 1)² = 400 + 40 + 1 = 441, using the first identity in your head. |
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Worked example 2 Question. Expand (x + 3)² using the identity.
Answer: (x + 3)² = x² + 6x + 9. |
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Worked example 3 Question. Use an identity to compute 49 × 51.
Answer: 49 × 51 = 2499. |
Practise with the interactive
Practise it: drag the area model to change a and b, and watch the square split into a², two ab pieces and b². The interactive opens right here in the lesson.
Practice set A, multiple choice
1. a(b + c) equals …
ab + ac, by the distributive law.
2. (a + b)² equals …
a² + 2ab + b².
3. (a + b)(a − b) equals …
a² − b², the difference of two squares.
4. (a − b)² equals …
a² − 2ab + b².
Practice set B, short answer
1. Expand (y − 4)².
| 1 | Use (a − b)² = a² − 2ab + b². y² − 2(y)(4) + 4². |
| 2 | Simplify. y² − 8y + 16. |
2. Expand (x + 7)(x − 7).
x² − 49, using the difference of two squares.
3. Find 102² using an identity.
| 1 | (100 + 2)² = 100² + 2(100)(2) + 2². 10000 + 400 + 4. |
| 2 | So. 10404. |
Quick summary
| Idea | The idea |
| Distributive | a(b + c) = ab + ac. |
| Two brackets | each term times each term. |
| Square of a sum | a² + 2ab + b². |
| Square of a difference | a² − 2ab + b². |
| Product of sum and difference | a² − b². |
| Use | fast mental arithmetic. |
| Open the Virtual Lab |
These free Grade 8 Maths revision notes explain the distributive law and the standard algebraic identities for squares, with clear step by step worked examples and labelled diagrams for every student following the new Ganita Prakash book.
© 2026 School Revise. All rights reserved. This lesson is original content written by School Revise, aligned to the CBSE and NCERT Class 8 Mathematics (Ganita Prakash) syllabus. Unauthorised copying, reproduction or redistribution is not permitted. Curriculum names are used only to indicate alignment.
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