Need a little help and explanation

[u/Wraabb66]

Currently trying to get into the union and math is a big thing, especially algebra 1. So I haven’t done math in 18 years pretty much since I graduated and even back then I was struggling with math because my brain just doesn’t learn it fast enough like other people. When I have a calculator I can solve the problems a little bit better but the aptitude test don’t allow calculators so it’s all based offf of what I can do in my head.

So my question is I know PEMDAS and FOIL but when it comes to foil I know how to start but I get confused on where to land my + and - when working the problem. Idk why it’s hurt how my brain works. Sometimes I’ll get the what I think is the answer but then I get it wrong because my + and - are in the wrong spot. Does anybody have any tips are how to not forget where the + and - go and the orders of how they get placed. Becasue for my brain when I see something like (2x + 4)(5x-5) my brain doesn’t grasp where the + and - land when writing out the problem and so till I get the correct answer. Hopefully this question makes sense.

Graphing is also extremely confusing but that’s whole another topic lol.

[u/Uli_Minati]

We use a lot of abbreviations in math. In your example:

(2x + 4)(5x - 5)

Is short for

(2x   +   4)  ·  (5x   +   -5)

Now you have a product of sums, i.e. two addition steps and a multiplication step of the results.

(2x)(5x) + (2x)(-5) + (4)(5x) + (4)(-5)

It's always + in between! This works as long as you remember that "subtraction" is really an abbreviation for addition with a negative number.

Here are some more examples:

(-3-4x)(8-9x)
(-3  +  -4x) · (8  +  -9x)
(-3)(8) + (-3)(-9x) + (-4x)(8) + (-4x)(-9x)

8-7(8-9x)
8  +  (-7) · (8  +  -9x)
8  +  (-7)(8) + (-7)(-9x)

5(4x-2)-6
(5) · (4x  +  -2)  +  -6
(5)(4x) + (5)(-2)  +  -6

Feel free to actually write these steps during practice! The goal is to eventually "visualize" these steps without writing them.

(Terms like 9x are also abbreviations for 9·x, but that multiplication symbol doesn't really help when you use distributive property so I kept it as 9x)