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# 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*}