Why $(x-5)^2-4$ can be factorised as $(x-5-2)(x-5+2)$ I would like to understand why $(x-5)^2-4$ can be factorised as $(x-5-2)(x-5+2)$
I am particularly concerned with the term, $-4$.

Note that

$$a^2-b^2=a^2-ab+ab-b^2=a(a-b)+b(a-b)=(a+b)(a-b)$$

Now put $a=(x-5)$ and $b=2$
$$(x-5)^2-4=(x-5)^2-2^2=((x-5)+2)((x-5)-2)=(x-5+2)(x-5-2)$$
