Understanding Factorising

  • Factorising is the process of breaking an algebraic expression into its simplest parts, called factors.
  • It’s the opposite of expansion: while expansion involves going from a compact form to an open one, factorising does the reverse.

Basic Factorising Techniques

  • Common factors: Start by looking for any common factors in the terms of the expression. For instance, in 4x + 8, the common factor is 4, so it can be factorised as 4(x + 2).
  • Difference of squares: Recognise that any expression in the form a^2 - b^2 can be factorised into (a + b)(a - b).
  • For instance, in x^2 - 4, x^2 is a^2 and 4 is b^2, so it can be factorised into (x + 2)(x - 2).

Factorising Quadratics

  • Simple Quadratics: Remember that quadratics of the form ax^2 + bx + c with a=1, can be factorised into (x + p)(x + q) where p and q are numbers that add up to b and multiply to c.
  • Complex Quadratics: If a ≠ 1, factorising becomes more complex and often involves the use of the quadratic formula -b ± sqrt(b^2 - 4ac) / 2a.

Your Final Tips

  • Practice factorising a wide range of expressions regularly so your skills stay sharp.
  • Always check your factorised solutions by expanding them out. If done correctly, you should arrive back at the original problem.
  • Remember: factorising is a critical skill in algebra, used in solving equations, simplifying expressions, and working with fractions.