Kidz Olympiad🎉

Mathematics Class 8 - Factorisation Notes

Comprehensive study notes for Class 8 - Factorisation olympiad preparation

Factorisation

Welcome to the chapter on Factorisation for Class 8. In this chapter, you will learn how to break algebraic expressions into their factors. By the end of this chapter, you will be able to factorise expressions and solve related problems with confidence!

Introduction

Factorisation means writing an algebraic expression as a product of its factors. Factors are expressions that multiply together to give the original expression.

Types of Factorisation

  • By taking out common factors
  • By grouping terms
  • By using identities
  • By splitting the middle term

1. Taking Out Common Factors

Find the common factor in each term and take it out.

  • Example: 6x + 12 = 6(x + 2)
  • Example: ab + ac = a(b + c)

2. Grouping Terms

Group terms to find common factors.

  • Example: ax + ay + bx + by = (ax + ay) + (bx + by) = a(x + y) + b(x + y) = (a + b)(x + y)

3. Using Identities

Use algebraic identities to factorise expressions.

  • a2 - b2 = (a - b)(a + b)
  • a2 + 2ab + b2 = (a + b)2

4. Splitting the Middle Term

For quadratic expressions, split the middle term to factorise.

  • Example: x2 + 5x + 6 = x2 + 2x + 3x + 6 = (x + 2)(x + 3)

Fun Activity: Factorisation Challenge!

Write five expressions and try to factorise them using different methods. Check your answers with your friends!

Summary

  • Factorisation breaks expressions into products of factors.
  • Use common factors, grouping, identities, or splitting the middle term.
  • Practice helps you master factorisation.

Practice Questions

  1. Factorise: 8x + 12y
  2. Factorise: x2 - 9
  3. Factorise: x2 + 7x + 10
  4. Factorise: ab + ac + db + dc
  5. Factorise: a2 + 2ab + b2

Challenge Yourself

  • Make your own quadratic expression and factorise it.
  • Factorise: 12xy + 18xz + 8y2 + 12yz

Did You Know?

  • Factorisation helps in solving equations and simplifying expressions!
  • It is used in higher mathematics and many real-life problems.

Glossary

  • Factor: A number or expression that divides another exactly.
  • Factorisation: Writing an expression as a product of its factors.
  • Identity: An equation that is true for all values of the variables.
  • Quadratic Expression: An expression of the form ax2 + bx + c.

Answers to Practice Questions

  1. 4(2x + 3y)
  2. (x - 3)(x + 3)
  3. (x + 2)(x + 5)
  4. (a + d)(b + c)
  5. (a + b)2

Practice factorisation to make algebra easy and fun!

Quick Navigation