<s>[INST] 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, $-4$.
 [/INST] Here's another way without using fancy formulas
$$ (x-5)^2-4 $$
$$=x^2-5x-5x+25-4 $$
$$=x^2-10x+25-4 $$
$$=x^2-10x+21 $$
$$=(x-3)(x-7) $$
$$=(x-5+2)(x-5-2) $$
</s>