Factorising Algebraic Expressions

What is Factorising?

• Factorising: Breaking something into its factors.
  • Example with numbers: 55 can be factorised into 5 x 11 or 1 x 55.
  • Example with algebraic terms: 3x can be factorised into 3 x x.

Factorising an Expression

• Involves taking out the highest common factor (HCF).
• Example: Factorise 3x + 15.
  • Factors of 3x: 3 and x.
  • Factors of 15: 1, 3, 5, 15.
  • HCF: 3
  • Factorise by dividing each term by 3:
    • [3x + 15 = 3(x + 5)]

Importance of Factorising

• Useful in simplifying expressions, especially when dealing with fractions and longer terms.
• Aids in solving equations and simplifying expressions.

More Examples

Expressions with Unknowns

• Example: 6ab - a²b

  • Factors of 6ab: 6, a, b.
  • Factors of a²b: a, a, b.
  • HCF: ab
  • [6ab - a²b = ab(6 - a)]

• Example: pqr + qrt - qsw

  • Common factor: q
  • [pqr + qrt - qsw = q(pr + rt - sw)]

Expressions with Numbers and Exponents

• Example: 25p² - 10p

  • Common factors: 5 and p
  • [25p² - 10p = 5p(5p - 2)]

• Example: 6p⁴ - 12p

  • Common factor between numbers: 6
  • Common factor for p: p
  • [6p⁴ - 12p = 6p(p³ - 2)]

Tips

• Always identify the highest common factor first.
• Divide each term by the HCF to simplify.
• Use factorising to simplify expressions before further operations or solving equations.