Okay, so to simplify the one that you just gave me, you're first going to distribute the 6x to both terms in the parentheses. So you end up with two answers which you'll stick back together to form the final answer.
6x * 3x = 18x^2
6x * -x = -6x^2
Stick them back together:
18x^2 - 6x^2
Now, you'll notice that they can be combined to give a final answer. If you had something like 18x^2 - 6x, you wouldn't be able to combine them because one is an x^2, and the other is a simple x.
So, just do simple subtraction, and you get 12x^2. So, 6x (3x -x) can be simplified to 12x^2.
Just something to note, whenever you've got two terms that can be combined in the parentheses (x and x, or x^2 and x^2, so on...), combine them before distributing the term outside the parentheses.
So, in this case, you'd actually have 6x(2x), and that simplifies to 12x^2.
As a more complex example, let's simplify 2x(3x^2 - 12).
2x * 3x^2 = 6x^3
2x * -12 = -24x.
6x^3 -24x | This is your final answer. Can't simplify an x^3 and an x beyond this point, so leave it at this.
A little more complex:
2x(3x^2 - 2) + 5x(2x^2 + 7)
Now you're going to distribute the two to the parentheses right next to it, and do the same with the 5. Then stick it all together, and combine like terms to get your final answer.
6x^3 -4x + 10x^3 + 35x
Combine like terms (the -4x and the 35x, and the 6x^3 and the 10x^3)
16x^3 + 31x
You can even do the same thing with x's and y's in the same equation, and I can give you a few examples and problems if you want. But for now, here are some problems to work:
1. 3x(10x - 12x^2) - 2x(2x + 4)
2. 2x(2x^400 + 12) + 2x(2x^399 +12)
3. 5x(10 + 12) - 6x(12x^2 - 10x)
Spoiler: (Highlight this box to see the hidden message.)
1. -36x^3 + 26x^2 - 8x
2. 4x^401 + 4x^400 +48x
3. -72x^3 + 60x^2 + 110x
Watch your signs. It may help to think of a negative like this:
3x(10x - 12x^2) + (-2x(2x +4))
Distribute the negative with the 2x, and you'll get the right sign every time.