How to factorise $(x-1)^2 - (x-5)^2$? My attempt: 
$a = (x-1)$ 
$c = (x-5)$
$a^2 - c^2$
which is equal to: 
$$((x-1) - (x-5))((x-1)+(x-5))$$
But the correct answer is : 
$8(x-3)$
Can you explain, please?

Your doing is correct, you just need to expand the expressions inside the parenthesis:
\begin{align}((x-1) - (x-5))((x-1)+(x-5))&=(x-1-x+5)(x-1+x-5)\\ & =4(2x-6)\\ & =8(x-3)\end{align}
