1. Because this product is composed of the
We note that the product of the two binomials has four terms – each of these is a partial product. We multiply each term of the first binomial by each term of the second binomial to get the four partial products.
F O I L
( a b )( c d ) = ac ad bc bd
Product of the FIRST terms of the binomials
Product of the OUTSIDE terms of the binomials
Product of the INSIDE terms of the binomials
Product of the LAST terms of the binomials
Because this product is composed of the
First, Outside, Inside, and Last terms,
this pattern is often referred to as FOIL method of multiplying two binomials.

2. Recall the distributive property of multiplication over addition . . .
symbolically:
a ( b + c) = ab + ac

3. using your mental math skills . . .
An example: 6 x 13
using your mental math skills . . .
symbolically:
6 (10 + 3) = 6(10) + (6)(3)

4. What about 12 x 23? Mental math skills?
(10+2)(20+3) = 10× ×3 + 2×20 + 2×3
200 30 40
+ 6
276

5. And now for multiplying binomials
(a+b)(c+d) = a(c+d) + b(c+d)
= ac + ad + bc + bd