Simplifying
(a + b)(c + d)

Multiply (a + b) * (c + d)
(a(c + d) + b(c + d))
((c * a + d * a) + b(c + d))
((ac + ad) + b(c + d))
(ac + ad + (c * b + d * b))
(ac + ad + (bc + bd))
(ac + ad + bc + bd)