Recall the distributive property of multiplication over addition . . .

1

• Recall the distributive property of
  multiplication over addition . . .
• symbolically
• a (b c) a b a c
• and pictorially (rectangular array area model)

b
c
a b
a c
a
2

• An example 6 x 13
• using your mental math skills . . .
• symbolically
• 6 (10 3) 6 10 6 3
• and pictorially (rectangular array area model)

10
3
6 10
6 3
6
3

• What about 12 x 23?
• Mental math skills?
• (102)(203) 1020 103 220 23

20
3
10 20
10
10 3
2 3
2
2 20
4

• And now for multiplying binomials
• (ab)(cd) a(cd) b(cd)
• ac ad bc bd

c
d
a c
a
a d
b d
b
b c
5
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. Note that each of these four
partial products represents the area of one of
the four rectangles making up the large rectangle.