# Thread: Help me! I'm so confused!

1. ## Help me! I'm so confused!

Hi guys, I was wondering if you can help me. I'm actually a student brushing up on the maths skills and I've come up against some BIG problems. I learn by examples, and I find it difficult to understand a theory unless it is explained word for word. I'm currently looking at basic Algebra, and finding it very difficult to grasp. Could someone please enlighten me? Here's my problem.....
-2[-3(x − 2y) + 4y]
The first thing we do is expand out the round brackets inside.
-3(x − 2y) = -3x − (-3)(2y) = -3x + 6y

Now I understand the order of operation, so I get that we should expand the brackets first. BUT, how does [-3(x − 2y) become -3x − (-3)(2y). There is now explanation on how or indeed why this is done. Fustratingly, this has holted my progress as I can't find the solution anywhere. Why is the -3 repeated? Why are only certain brackets removed? What secretive rule is alludes me? I don't understand it at all.

As you can see the problem becomes a lot more complex, but I think if I had the rules to follow I would be able to tackle it.

The negative times negative in the middle gives positive 6y.
Remembering the -2 out front, our problem has become:
-2[-3(x − 2y) + 4y] = -2[-3x + 6y + 4y]
Now we collect together the y terms inside the [ ] square brackets:
[-3x + 6y + 4y] = [-3x + 10y]
Now we need to multiply by the -2 out the front:
= -2[-3x + 10y]
Taking each term one at a time:
(-2)(-3x) = 6x (Two negative numbers multiplied together give a positive); and
(-2)(10y) = -20y (Negative times positive gives negative)
Go back to the section on Integers if you are not sure about multiplying with negative numbers.
So the last step is:
-2[-3x + 10y] = 6x − 20y
So here's the summary of what we have done:
-2[-3(x − 2y) + 4y]
= -2[-3x + 6y + 4y]
= -2[-3x + 10y]
= 6x − 20y

2. BUT, how does [-3(x − 2y) become -3x − (-3)(2y).
Because multiplication is distributive. Consider this example (I gave a numerical expression to make it clearer):
$2(3) = 6$
$2(1+2) = 2(1)+2(2) = 2+4 = 6$

As you can see, if I am to rewrite 3 in an equivalent form (1+2) and multiply it by 2 by distributing it, I still get the same answer.

Another example:
$8(9) = 72$
$8(10-1) = 8(10)-8(1) = 80-8 = 72$

To sum up:
$a(b+c) = ab+ac$

3. I kind of see where your going now. When you say multiplication is distributive you mean (in the example of [-3(x − 2y) That -3 must be multiplied by both x and 2y. Making the result -3x − (-3)(2y). Is that right? You have at least cleared up the most difficult question. I need to know these things! Why was I never told!? Thanks anyway. I'll endever to conquer this one. Any more questions and I'll know where to come!