March 30, 2011
Lesson 10.3
Special Products of Polynomials
Multiply (a + b) times (a − b) using FOIL.
(a + b)(a − b) = a2 − b2
This pattern is called a difference of squares.
Why is that?
Binomial pairs of the form (a + b) and (a − b)
are called conjugates.
Simplify each using a special product rule.
1
March 30, 2011
Multiply (a + b) times (a + b) using FOIL.
Multiply (a − b) times (a − b) using FOIL.
These patterns result in perfect square trinomials.
(a + b)2 = a2 + 2ab + b2
(a − b)2 = a2 − 2ab + b2
Notice that the middle term in the trinomial is always
twice the product of the terms in the binomial.
Simplify each using a special product rule.
2
March 30, 2011
Rewrite the product 107 ⋅ 93 using a special
product rule. Then simplify without your
calculator.
The floor plan of a home is shown below.
Find an expression for the area of the
home.
3
March 30, 2011
Find a polynomial expression for the area
of each polygon.
Find an expression for the volume of the
box.
4