Factorising is the reverse of calculating the product of factors. In order to factorise a quadratic, we need to find the factors which, when multiplied together, equal the original quadratic.

Consider a quadratic expression of the form $a{x}^{2}+bx$. We see here that $x$ is a common factor in both terms. Therefore, $a{x}^{2}+bx$ factorises as $x(ax+b)$. For example, $8{y}^{2}+4y$ factorises as $4y(2y+1)$.

Another type of quadratic is made up of the difference of squares. We know that:

\[\begin{equation*}

(a+b)(a-b)={a}^{2}-{b}^{2}

\end{equation*}\]

So $a^2-b^2$ can be written in factorised form as $(a+b)(a-b)$.

This means that if we ever come across a quadratic that is made up of a difference of squares, we can immediately write down the factors.