Simplify m - {n - [p + (m + n - p)]}?

m-{n-[p+m+n-p]}
m-{n-{m+n]}
m-{n-m -n}
m-{-m}
=2m

= m - (n - [p + {m + n - p}])
= m - (n - [p + m + n - p])
= m - (n - [m + n])
= m - (n - m - n)
= m - (- m)
= m + m
= 2m

Answer: 2m

m - {n - [p + (m + n - p)]}
m - {n - [p + m + n - p]}
m - {n - [m + n]}
m - {n - m - n}
m - {- m}
m + m
2m

^_^

Start with the inmost expression and work you way outward.

[p + (m + n - p)]

These parentheses can just be removed. Adding an expression doesn't change the sign of anything inside the expression.

[p + (m + n - p)] = [p + m + n - p]

Now you can rearrange to get like terms together
= [p - p + m + n] = [m + n]

Next:
{n - [p + (m + n - p)]} = {n - [m + n]}

Subtracting does change the sign, because it's the same as
{n + (-1)*[m + n]} = {n + (-m) + (-n)}
or
{n - [m + n]} = {n - m - n}
So the short cut is just to change the sign of everything inside the brackets.

Now this can be rearranged since we've removed the brackets.

{n - [p + (m + n - p)]}
= {n - [m + n]} = {n - m - n} = {n - n - m} = {-m}

Finally:

m - {n - [p + (m + n - p)]} = m - {-m}

The minus sign gets applied to everything in the brackets

m - {-m} = m + m

m - {n - [p + (m + n - p)]}
m - {n - [p + m + n + p]}
m - {n - p - m - n - p}
m - n + p + m + n + p
2m + 2p

m - {n - [p + (m + n - p)]}
= m - n + [p + (m + n - p)]
= m - n + p + (m + n - p)
= m - n + p + m + n - p
= m + m - n + n + p - p
= 2m

Here you need to distribute each negative / positive sign into the bracket that follows:

m - {n - [p + (m + n - p)]}
m - {n - [p + m + n - p]}
Here the p's cancel:
m - {n - [m + n]}
m - {n - m - n}
Here the n's cancel:
m - {-m}
= 2m

start frm the inner bracket

P + m + n - p = m + n

n - m + n = -m

m - -m = 2m