1. DO NOW: Simplify. Topic: Algebraic Expressions 2
Aim: How do we multiply/divide a
polynomials by a monomial?
DO NOW: Simplify.
(A)
(2x3y)(-3x4y)
(B)
45x4y
(C)
(-x7y)(-y2z)
5xy

2. Review: Multiply Monomials
(-2x5y)(4x4yz)
Step 1
Multiply the coefficients
Step 2
Add exponents of like 
bases and keep the base

3. Example: 2x2y(3xy4 - 2) Multiplying a Polynomials by a Monomial
Use the DISTRIBUTIVE property to
multiply all terms in parenthesis by the term outside the 
parenthesis.
Example: 2x2y(3xy4 - 2)

4. Multiplying Polynomials by Monomials
DISTRIBUTIVE PROPERTY!!
Multiply using the _________________________ #1
2(4x + 3) #3
-2(3x - 5) #2
-2(x + 4)

5. Multiplying Polynomials by Monomials
DISTRIBUTIVE PROPERTY!!
Multiply using the _________________________
#4) 2x(-8x + 5x2 + y2)
#5) -5x(2x3 + 2x2 - 4)

6. Review: Dividing Monomials
24x14y15z4
6x7y5z4
Step 1
Divide coefficients
Step 2
Subtract exponents of like 
bases, keeping the base
****
Remember that terms do not 
"cancel". They reduce to 1.

7. Dividing Polynomials by Monomials
Can we use our knowledge of multiplying polynomials by monomials to help us?
Can we use our knowledge of dividing monomials to help us?

8. Dividing a Polynomial by a Monomial
Divide each term in the numerator by the monomial in the 
denominator.
**Remember that terms do not "cancel". They reduce to 1.
Example:

9. Distributive Property
Divide Polynomials by Monomials 
Using the ________________________________ #6 #7

10. Distributive Property
Divide Polynomials by Monomials 
Using the ________________________________ #9 #8

11. What is the rule when multiplying monomials?
SUMMARY
What is the rule when multiplying 
monomials?
What are the rules for dividing
monomials?
What property must we use to multiply or divide a 
polynomial by monomial?
Do terms ever "cancel'? Explain.

12.  
HOMEWORK
Complete Handout

13. Real-Life Applications!
#10) Your favorite sport is 
basketball. You decide you want to 
know the AREA of the court that you 
plan on. The length of the court is 
x inches and width is (3x + 7) inches. 
What is the AREA of the basketball 
court expressed as a polynomial in 
simplest form?
AREA FORMULA:_______________

14. Real-Life Applications!
#11) You have fenced off a 
rectangular play field in your 
backyard for your new puppy. The 
length of the play field is x and the 
width is (x + 5).
(a) What is the AREA of the play field expressed in simplest terms?
(b) What is the PERIMETER of the play field expressed in simplest 
terms?

15. Real-Life Applications!
#12) Your town has decided to get a 
new outdoor swimming pool. The 
length of the pool is x feet and the 
width of the pool is (x2 + 5x + 4) feet. What is the AREA of the 
swimming pool as a polynomial in 
simplest form?
AREA FORMULA:_______________