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