# Methods of factorisation: difference of two squares

Factorising an expression is simple if it is of the form $$A^2 -B^2$$. This is called the difference of two squares

$$A$$ and $$B$$ could be any algebraic expressions or numbers, so sometimes it is tricky to spot expressions of this kind.

Expressions of the form $$A^2-B^2$$ always factorise into the expression $$(A+B)(A-B)$$

1. Factorise $$a^4-25$$.

We spot that both $$a^4$$ and $$25$$ are squares. We take their square roots and fill in the difference of two squares formula.

$$$a^4-25 = (a^2+5)(a^2-5) $$$2. Factorise $$2xy^6-72x$$.

At first these do not look like squares, so it seems that we cannot factorise using the difference of two squares.

But if we try factoring out the common factor of $$2x$$, the task becomes easier. \begin{align*} 2xy^6-72x = 2x(y^6-36) &=2x((y^3)^2-6^2)\\ &= 2x(y^3+6)(y^3-6) \end{align*}