-a-(b-a-c)
=-a-b+a+c
=[-a+a]-b+c
=0-b+c
=-b+c
-(a-c)-(a-b+c)
=-a+c-a+b-c
=0+0+b
=b
b-(b+a-c)
=b-b-a+c
=0-a+c
=-a+c
(a-b+c)-(a+b+c)
=a-b+c-a-b-c
=[a-a]+[c-c]-b-b
=0+0-b-b
=0-b-b
=-b-b
a) -a - ( b - a - c )
= -a - b + a + c
= ( -a + a ) -b + c
= 0 - b + c
= -b + c
b) - ( a - c ) - ( a - b + c )
= -a + c - a + b - c
= ( -a - a ) + ( c - c ) + b
= 2 . ( -a ) + b
c) b - ( b + a - c )
= b - b - a + c
= 0 - a + c
= -a + c
d) ( a - b + c ) - ( a + b + c )
= a - b + c - a - b - c
= a + ( -b ) + c + ( -a ) + ( -b ) + ( -c )
= [ a + ( -a ) ] + [ ( -b ) + ( -b ) ] + [ c + ( -c ) ]
= 0 + 2 . ( -b ) + 0
= 2 . ( -b )