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