Example:
(a + b) (c + d)
First, use the distributive law and distribute the first factor over the second:
(a + b) (c + d)
equals
(a + b) c + (a + b)d
Now, distribute the c over (a + b):
(a + b) c + (a + b)d
equals
ac + bc + (a + b)d
Finally, distribute the d over (a + b):
ac + bc + (a + b)d
equals
ac + bc + ad + bd
So, we have found out:
(a + b) (c + d)
equals
ac + bc + ad + bd