1
5.4

• Special Products

2
The FOIL Method

• When multiplying two binomials, the distributive
  property can be easily remembered as the FOIL
  method.
• F product of First terms
• O product of Outside terms
• I product of Inside terms
• L product of Last terms

3
Using the FOIL Method
Example
Multiply (y 12)(y 4).
(y 12)(y 4)
Product of First terms is y2
(y 12)(y 4)
Product of Outside terms is 4y
(y 12)(y 4)
Product of Inside terms is 12y
(y 12)(y 4)
Product of Last terms is 48
F O I L
(y 12)(y 4) y2 4y 12y 48

• y2 8y 48

4
Using the FOIL Method
Example
Multiply (2x 4)(7x 5).
(2x 4)(7x 5)
14x2 10x 28x 20
14x2 18x 20
We multiplied these same two binomials together
in the previous section, using a different
technique, but arrived at the same product.
5
Squaring a Binomial

• Squaring a Binomial
• A binomial squared is equal to the square of the
  first term plus or minus twice the product of
  both terms plus the square of the second term.
• (a b)2 a2 2ab b2
• (a b)2 a2 2ab b2

Example Multiply (12a ? 3)2.
(12a ? 3)2
(12a)2 ? 2(12a)(3) (3)2
144a2 ? 72a 9
6
Sum and Difference of Two Terms

• Multiplying the Sum and Difference of Two Terms
• The product of the sum and difference of two
  terms is the square of the first term minus the
  square of the second term.
• (a b)(a b) a2 b2

Example Multiply (5a 3)(5a ? 3).
(5a 3)(5a ? 3)
(5a)2 ? 32
25a2 ? 9
7
Special Products

• Although you will arrive at the same results for
  the special products by using the techniques of
  this section or last section, memorizing these
  products can save you some time in multiplying
  polynomials.