Solve the following algebraic expression:[5z-(x+2y)]-[3x-(y-2z)]

This expression is testing your knowledge of the order of operations and the concept of like terms.  The order of operations states that you should work from the inside out when removing grouping symbols.  Basically, if a negative occurs in front of a grouping symbol, meaning (), {}, [], etc., it is telling you to take the negative sign into the grouping symbol.   This process changes the sign of everything inside the grouping symbols. 

Additionally, you have to remember the basic rules of multiplying negatives and positives.  If you are multiplying a negative and a negative you answer will be positive. Likewise, negative times a positive will give you a negative answer.  Basically the rules mean: If you have an odd number of negative signs in your multiplication problem you will have a negative answer and an even number of negative signs will yield a positive answer.  Your expression would be simplified as follows:

[5z – (x + 2y)] – [3x –(y – 2z)]   be careful with your signs

[5z – x – 2y] – [3x – y + 2z]  drop the first grouping symbol

                                        and apply the negative the

                                         second

5z – x – 2y – 3x + y – 2z        rearrange your like terms and

                                          combine

5z – 2z – x – 3x – 2y + y

3z - 4x - y