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

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

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)

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

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

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.

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?

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:

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

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

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.

  HOMEWORK Complete Handout

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:_______________

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?

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:_______________