a) (a - b) + (c - d) = a - b + c - d = (a + c) - (b + d)
b) (a - b) - (c - d) = a - b - c + d = (a + d) - (b + c)
c) -(-a + c - d) - (c -a + d) = a - c + d - c + a - d = 2(a - c)
d) -(a + b - c + d) + (a - b - c - d) = -a - b + c - d + a - b - c - d = 0
e) a(b - c - d) - a(b + c - d) = ab - ac - ad - ab - ac + ad = 0