How do i do "factoring" and the "distributive property"

if middle school is this confusing highschool will probably make me insane

The distributive property is just one of those things that you will have to accept without a proof (called on "axiom"). The property is basically


This works even if we substitute numbers.
2(4 + 6) = 2*4 + 2*6 = 8 + 12 = 20

You can prove this by doing it another away:
2(10) = 20

Factoring is the opposite of distributing. If you have
xy + xz,
then you see that each term has an x in it. xy has an x and xz has an x. Then you can factor ("take out") an x because both have an x in them.
xy + xz becomes x(y + z)

You can prove this with the distributive property because if you distribute the x, it becomes xy + xz again.

I hope I helped at least a little.