SIMPLIFY: 2x+3y-z-{x+3y-[y+2z-(x-2y-4z)]}

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You need to open the brackets moving from inside to outside such that:

`2x+3y-z-{x+3y-[y+2z-(x-2y-4z)]} = 2x+3y-z-[x+3y-(y+2z-x+2y+4z)]`

`2x+3y-z-[x+3y-(y+2z-x+2y+4z)] = 2x+3y-z-(x+3y-y-2z+x-2y-4z)` `2x+3y-z-(x+3y-y-2z+x-2y-4z) = 2x+3y-z-x-3y+y+2z-x+2y+4z`

Notice that minus sign in front of brackets changes the sign of each term inside brackets when you open the brackets.

You need to collect like terms such...

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You need to open the brackets moving from inside to outside such that:

`2x+3y-z-{x+3y-[y+2z-(x-2y-4z)]} = 2x+3y-z-[x+3y-(y+2z-x+2y+4z)]`

`2x+3y-z-[x+3y-(y+2z-x+2y+4z)] = 2x+3y-z-(x+3y-y-2z+x-2y-4z)` `2x+3y-z-(x+3y-y-2z+x-2y-4z) = 2x+3y-z-x-3y+y+2z-x+2y+4z`

Notice that minus sign in front of brackets changes the sign of each term inside brackets when you open the brackets.

You need to collect like terms such that:

`(2x - x - x) + (3y- 3y + y + 2y) + (-z + 2z + 4z)`

`0 + 3y + 5z`

Hence, simplifying the algebraic expression yields `2x+3y-z-{x+3y-[y+2z-(x-2y-4z)]} = 3y + 5z.`

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