Class 8 Maths — Chapter 6: We Distribute, Yet Things Multiply

What you'll learn

• ▸The Distributive Property
• ▸Analyzing Changes in Products
• ▸Multiplying Two Binomials (General Form)
• ▸Handling Subtraction in Binomial Multiplication
• ▸Combining Like Terms after Expansion
• ▸Multiplying a Monomial by a Polynomial
• ▸Multiplying Complex Polynomials

Chapter Summary

--- PAGE 1 --- WE DISTRIBUTE, YET THINGS MULTIPLY We have seen how algebra makes use of letter symbols to write general statements about patterns and relations in a compact manner. Algebra can also be used to justify or prove claims and conjectures (like the many properties you saw in the previous chapter) and to solve problems of various kinds. Distributivity is a property relating multiplication and addition that is captured concisely using algebra. In this chapter, we explore different types of multiplication patterns and show how they can be described in the language of algebra by making use of distributivity. 6.1 Some Properties of Multiplication Increments in Products Consider the multiplication of two numbers, say, 23 × 27. ? 1. By how much does the product increase if the first number (23) is increased by 1? ? 2. What if the second number (27) is increased by 1? ? 3. How about when both numbers are increased by 1? ? Do you see a pattern that could help generalise our …

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Explain distributivity simply. Get Solution →
2. Give real examples of algebra. Get Solution →
3. Quiz me on multiplying numbers. Get Solution →
4. According to the text, what is the distributive property of multiplication over addition? Get Solution →
5. What does the chapter define as 'like terms'? Get Solution →
6. By how much does the product `ab` increase if only the number `b` is increased by 1? Get Solution →
7. What is the result of expanding (a + b)(a + b) as shown in the chapter? Get Solution →
8. What is the increase in the product `ab` when both `a` and `b` are increased by 1? Get Solution →

Did you know?

• 💡 The word 'algebra' comes from the Arabic 'al-jabr', meaning 'reunion of broken parts'.
• 💡 Ancient Egyptians multiplied by repeatedly doubling numbers, not using traditional multiplication tables.
• 💡 A googol is the number 1 followed by 100 zeros, showing how fast numbers can multiply.
• 💡 Algebra is used by engineers to design bridges and doctors to calculate medicine dosages.
• 💡 Some numbers, like 6 and 28, are 'perfect numbers' because their divisors add up to themselves.

Frequently Asked Questions

Related Chapters