# Factorising

# 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.