At the minute I am going through algebra, Whenever I come to something new or something I dont yet understand fully(I can do the algorithm most times, but maybe not understand the why of it), I make a point of spending the time to understand the why and how something works, even as basic as why Negative * Negative = Positive etc.
Today I was going through basic factorisation(I.e: $4x(4+3y)$ when I hit a road block, I couldn't understand for example: how to factorise: $49x^2 + 100y^2$ And when I seen the answer it baffled me even more. so I realised I need to learn quadratic factorisation.
So today when I was trying to learn it I just couldn't understand why it works or how to make my own quadratic factorisations.
So my question is, do I need to understand it, or can I get away of just "doing it" like following the algorithms/methods?
You should understand factoring!
It sounds like you're confused about why, for example, $(7x + 10y) * (7x-10y) = 49x^2 - 100y^2$.
The good news is, if you trust the distributive property, which says $A*(B+C) = A*B + A*C$, it's easy to understand why this kind of factoring works. You just have to apply the distributive property a few times in a row:
$(7x + 10y) * (7x-10y)$
$= (7x + 10y) * (7x) + (7x + 10y) * (-10y)$
$= (7x) * (7x + 10y) + (-10y) * (7x + 10y)$
$= (7x * 7x + 7x * 10y) + (-10y * 7x + -10y*10y)$
$=(49x^2+70xy) + (-70xy -100y^2)$
$= 49x^2 - 100y^2$
There are some tricks for guessing what the factored form (the one with the parentheses) looks like, but this should explain why it works!