How do you factor ax-xb-ay plus yb?

Answer 1

Recall distributivity a(b + c) = ab + ac = (b + c)a

and associativity (ab)c = a(bc) (a + b) + c = a + (b + c)

as well as commutativity ab = ba a + b = b + a

we are gonna need those. See for yourself when I applied each to learn the trick:

ax - bx - ay + yb = (ax - bx) + (-ay + yb) = x(a - b) + -y(a - b) = (x - y)(a - b)