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 − 20ySo here's the summary of what we have done:
-2[-3(x − 2y) + 4y]
= -2[-3x + 6y + 4y]
= -2[-3x + 10y]
= 6x − 20y