simplify
z-(2z-[3z-(4z-5z)-6z0-7z]-8z
Check for a typo:
I will assume that -6z0 is supposed to be -6z
You also have one ( bracket which is not closed, I will assume it closes after the -8z .
z-(2z-[3z-(4z-5z)-6z-7z]-8z)
= z-(2z-[3z-4z+5z-6z-7z]-8z)
= z - (2z -[-9z] -8z)
= z - (2z+9z-8z)
= z - (3z)
= -2z
To simplify the given expression, let's break it down step by step:
Step 1: Simplify the innermost parentheses.
Inside the innermost parentheses, we have (4z-5z), which equals to -z:
z-(2z-[3z-(-z)-6z-7z]-8z)
Simplified expression: z-(2z-[3z+z-6z-7z]-8z)
Step 2: Simplify the next level of parentheses.
Now, inside the next set of parentheses, we have [3z+z-6z-7z]. Let's combine the z terms:
z-(2z-[3z+z-6z-7z]-8z)
Simplified expression: z-(2z-[2z-13z]-8z)
Step 3: Combine like terms.
Inside the remaining set of parentheses, we have [2z-13z]. Let's combine the z terms:
z-(2z-(-11z)-8z)
Simplified expression: z-(2z+11z-8z)
Next, combine like terms:
Simplified expression: z-(5z)
Step 4: Distribute the negative sign.
To distribute the negative sign, we change the sign of each term inside the parentheses:
z-5z
Now, combine like terms:
Simplified expression: -4z
Therefore, the simplified expression for z-(2z-[3z-(4z-5z)-6z0-7z]-8z) is -4z.