a: a(b+c)-b(a-c)
=ab+ac-ab+bc
=ac+bc=c(a+b)
a: a(b-c)-a(b+d)
=ab-ac-ab-ad
=-ac-ad=-a(c+d)
a: (a-b)-(c-d)+(b+c)
=a-b-c+d+b+c
=a+d
b: (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)
b: (a-b)+(c-d)-(a+c)
=a-b+c-d-a-c
=-b-d
=-(b+d)
