a) \(\left(a+b+c\right)-\left(a-b+c\right)=a+b+c-a+b-c=2b\)
b) \(\left(a+b-c\right)+\left(a-b\right)-\left(a-b-c\right)=a+b-c+a-b-a+b+c\)
\(=a+b\)
c) -(a-b-c)+(-a+b-c)-(-a-b+c) = -a+b+c-a+b-c+a+b-c = -a+3b-c
a, ( a + b + c ) - ( a - b + c )
= a + b + c - a + b - c
= 2b
b, ( a + b - c ) + ( a - b ) - ( a - b - c )
= a + b - c + a - b - a + b + c
= a + b
c, - ( a - b - c ) + ( - a + b - c ) - ( - a - b + c)
= - a - b - c - a + b - c + a - b + c
= a - b - c
\(a) \) \((a+b+c)-(a-b+c)\)
\(=a+b+c-a+b-c\)
\(=(a-a)+(b+b)+(c-c)\)
\(=0+b+b+0\)
\(=2b\)
\(b)\) \((a+b-c)+(a-b)-(a-b-c)\)
\(=a+b-c+a-b-a+b+c\)
\(=(a+a-a)+(b-b+b)-(c-c)\)
\(=a+b\)
\(c) \) \(-(a-b-c)+(-a+b-c)-(-a-b+c)\)
\(=-a+b+c-a+b-c+a+b-c\)
\(=-(a+a-a)+(b+b+b)-(c-c+c)\)
\(=-a+3b-c\)