# 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)`.

• 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`.