1. § 5.2
Multiplication of Polynomials

2. Multiplying Polynomials
EXAMPLE
Multiply
SOLUTION
Rearrange factors
Multiply coefficients and
add exponents
Simplify
Blitzer, Algebra for College Students, 6e – Slide #2 Section 5.2

3. Multiplying Polynomials
EXAMPLE
Multiply
SOLUTION
Distribute
Multiply coefficients and
add exponents
Blitzer, Algebra for College Students, 6e – Slide #3 Section 5.2

4. Multiplying Polynomials
EXAMPLE
Note this: We multiply each term of the binomial by each term of the trinomial. We get 6 products in all.
Multiply
SOLUTION
Multiply the trinomial by each term of the binomial
Distribute
Multiply coefficients and
add exponents
Simplify
Blitzer, Algebra for College Students, 6e – Slide #4 Section 5.2

5. Using the FOIL Method to Multiply Binomials
Multiplying Polynomials - FOIL
Using the FOIL Method to Multiply Binomials
last F O I L
first
inside
Product of First terms
Product of Outside terms
Product of Inside terms
Product of Last terms
outside
Blitzer, Algebra for College Students, 6e – Slide #5 Section 5.2

6. Multiplying Polynomials - FOIL
EXAMPLE
Multiply
SOLUTION
last F O I L
first
Multiply
inside
outside
Combine like terms
Blitzer, Algebra for College Students, 6e – Slide #6 Section 5.2

7. Multiplying Polynomials – Special Formulas
The Square of a Binomial Sum
The Square of a Binomial Difference
The Product of the Sum and Difference of Two Terms
Blitzer, Algebra for College Students, 6e – Slide #7 Section 5.2

8. Multiplying Polynomials – Special Formulas
EXAMPLE
Multiply
SOLUTION
Use the special-product formula shown. +
= Product
Blitzer, Algebra for College Students, 6e – Slide #8 Section 5.2

9. Multiplying Polynomials – Special Formulas
EXAMPLE
Multiply
SOLUTION
Use the special-product formula shown. - +
= Product
Blitzer, Algebra for College Students, 6e – Slide #9 Section 5.2

10. Multiplying Polynomials – Special Formulas
EXAMPLE
Multiply
SOLUTION
Use the special-product formula shown. - =
First Term Squared
Second Term Squared
Product =
Blitzer, Algebra for College Students, 6e – Slide #10 Section 5.2

11. Multiplying Polynomials – Special Formulas
EXAMPLE
Multiply
SOLUTION
We can group the terms so that the formula for the square of a binomial can be applied.
(A + B) (A - B) =
Blitzer, Algebra for College Students, 6e – Slide #11 Section 5.2

12. Multiplying Polynomial Functions
EXAMPLE
(a) (fg)(x)
(b) (fg)(-1)
(c) (fg)(0)
SOLUTION
(a) (fg)(x) = f (x) g(x)
Thus,
= (x - 4)(x + 10) F O I L
Blitzer, Algebra for College Students, 6e – Slide #12 Section 5.2

13. Multiplying Polynomial Functions
CONTINUED
(b) We use the product function to find (fg)(-1) – that is, the value of the function fg at -1. Replace x with -1.
(c) We use the product function to find (fg)(0) – that is, the value of the function fg at 0. Replace x with 0.
Blitzer, Algebra for College Students, 6e – Slide #13 Section 5.2

14. Multiplying Polynomial Functions
EXAMPLE
SOLUTION
To find f (a + h) – f (a), we first replace each occurrence of x with a + h and then replace each occurrence of x with a. Then we perform the resulting operations and simplify.
f (a + h) – f (a)
Use , replacing x with a + h and a, respectively.
Blitzer, Algebra for College Students, 6e – Slide #14 Section 5.2

15. Multiplying Polynomial Functions
CONTINUED
Multiply as indicated
Multiply
Combine like terms
Blitzer, Algebra for College Students, 6e – Slide #15 Section 5.2