Go back to Order of Operations if you are not sure what to do first with this question.

-2[-3(x − 2y) + 4y]

The square brackets [ ] work just the same as round brackets ( ). We could have used curly brackets { } here as well.

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

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

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

Note:

The fancy name for round brackets ( ) is "parentheses".

The fancy name for square brackets [ ] is "box brackets".

The fancy name for curly brackets { } is "braces".