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* − 2*y*) + 4*y*]

The first thing we do is expand out the round brackets inside.

-3(*x* − 2*y*) = -3*x* − (-3)(2*y*) = -3*x* + 6*y*

Now I understand the order of operation, so I get that we should expand the brackets first. BUT, how does [-3(*x* − 2*y*) become -3*x* − (-3)(2*y*). 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 6*y.*

Remembering the -2 out front, our problem has become:

-2[-3(*x* − 2*y*) + 4*y*] = -2[-3*x* + 6*y* + 4*y*]

Now we collect together the *y* terms inside the [ ] square brackets:

[-3*x* + 6*y* + 4*y*] = [-3*x* + 10*y*]

Now we need to multiply by the -2 out the front:

= -2[-3*x* + 10*y*]

Taking each term one at a time:

(-2)(-3*x*) = 6*x* (Two negative numbers multiplied together give a positive); and

(-2)(10*y*) = -20*y* (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[-3*x* + 10*y*] = 6*x* − 20*y*

So here's the **summary** of what we have done:

-2[-3(*x* − 2*y*) + 4*y*]

= -2[-3*x* + 6*y* + 4*y*]

= -2[-3*x* + 10*y*]

= 6*x* − 20*y*

Please Help!!!!