Lecture on Factorising Algebraic Expressions

Introduction to Factorising

• Definition: Factorising is breaking something into its factors.
• Example: Factorising number 55 into 5 x 11 or 1 x 55.

Factorising Algebraic Terms

• Example: 3x can be factorised into 3 x x.
• Highest Common Factor (HCF): Key for factorising expressions.

Factorising Expressions

• Example: Factorise 3x + 15.
  • Break down: 3x = 3 x x; 15 = 1 x 15 or 3 x 5.
  • HCF is 3.
  • Factorised form: 3(x + 5).

Importance of Factorising

• Simplifies expressions, especially useful in fractions, longer terms, and equations.
• Helps in canceling terms to simplify expressions.

Examples of Factorising

1. Expression: 6ab - a^2b

   • Factors: 6ab = 6 x a x b; a^2b = a x a x b.
   • Common Factors: a and b.
   • Factorised Form: ab(6 - a).

2. Expression: pqr

   • Common Factor: q.
   • Factorised Form: q(pr + rt - sw).

3. Expression: 25p^2 - 10p

   • Factors: 25 = 5 x 5; 10 = 5 x 2.
   • Common Factor: 5p.
   • Factorised Form: 5p(5p - 2).

4. Expression: 6p^4 - 12p

   • Factors: 6 and 12 have a common factor of 6.
   • Common Factor: 6p.
   • Factorised Form: 6p(p^3 - 2).

Double Checking Factorisation

• Expand the factorised expression to verify correctness.
• Example: Expanding ab(6 - a) returns the original expression 6ab - a^2b.

Conclusion

• Factorisation is a crucial skill for simplifying algebraic expressions.
• Practice with different types of expressions to gain proficiency.
• Feel free to ask questions for clarification.

This concludes the lecture on factorising algebraic expressions. Please review these notes and practice more problems to solidify your understanding.