Math 10C
Polynomials: Lesson #3
Multiplying Binomials
Objective: By the end of this lesson, you will be able to:
- Multiply two binomials concretely, pictorially, and symbolically
- Verify a polynomial multiplication
- Use patterns to multiply perfect squares and conjugates
We can extend our knowledge of multiplying by a monomial to multiplying two binomials.
1. Using algebra tiles (concretely).
2. Using drawings to represent algebra tiles (pictorially).
e.g. 1) Find the product of x  23x  2 by drawing algebra tiles.
3. Using a multiplication grid (symbolically):



e.g. 1) Multiply y 2  5 y 2  8 using a multiplication grid:
Notice: Using a multiplication grid, we can multiply polynomials of any degree.
Math 10C
Polynomials: Lesson #3
4. Using algebraic symbols (symbolically):
We need to expand the idea of the distributive property in order to multiply binomials.
Notice: In the multiplication grid, we multiplied ___________ terms in one binomial by
___________terms in the other binomial to get __________ products.
We can do the same thing using the acronym ____________.
FOILe.g. 3) Use FOIL to find the product of the following binomials:
a) n  3m6n  5m
b) 9  x 3x  4
e.g. 4) Verify your solution for e.g. 3b) by substituting the value x  2 .
e.g. 5) a) Find the area of the rectangle shown below.
2y  8
3y  1
Math 10C
Polynomials: Lesson #3
b) What is the area of the rectangle if y  15 cm?
Special Binomial Products
1. The square of a binomial:
a  b2 
Important: a  b  
2
a  b2 
e.g. 6) Expand and simplify 5 x  3 y  :
a) Using FOIL
2
2. The product of conjugates:
Conjugates are:
a  ba  b 
b) Using the perfect squares pattern
Math 10C
Polynomials: Lesson #3
e.g. 7) Find the product of 10 x  710 x  7 :
a) Using FOIL
Assignment:
p. 166-167 #4, 12
p. 177 #5, 10
p. 194-195 #4
b) Using the conjugates pattern