Factorising Techniques

The key to factorising is finding what's common between terms and pulling it out front. Start by looking for the highest common factor (HCF) of all the numbers and variables.

For simple expressions like 4x + 12, find the HCF of 4 and 12, which is 4. Then factor out: 4$x + 3$. With variables involved, like 3x² + 6x, you factor out both numbers and variables: 3x$x + 2$.

When you've got multiple variables like 6x²y + 3xy, look for the HCF of everything. Here it's 3xy, giving you 3xy$2x + 1$. Always check your answer by expanding it back out.

Quick Check: After factorising, multiply your brackets back out to make sure you get the original expression!

The difference of two squares is a special pattern: x² - y² = $x - y$$x + y$. So 4x² - 9 becomes $2x - 3$$2x + 3$ because 4x² = (2x)² and 9 = 3².