Title: Algebra 1
Author: Mandy McDaniel
Last saved by: Glencoe Mathematics

Lesson 7-5

Example 1 Multiply a Polynomial by a Monomial
Find 3xy(2x – y – 1)
Method 1	Horizontal
3xy(2x – y – 1) = 3xy(2x) – 3xy(y) – 3xy(1)	Distributive Property
  = 6xy – 3xy– 3xy	Multiply.

Method 2	Vertical
           2x – y – 1
()                3xy		Distributive Property
6x^2y – 3xy^2– 3xy	Multiply.

Example 2 Simplify Expressions
Simplify b(2b – 4) + 4(b^2 – 6b – 3).
b(2b – 4) + 4(b^2 – 6b – 3)
= b(2b) –b(4) + 4(b^2) – 4(6b) – 4(3)	Distributive Property
= b – 2b + 4b^2 – 24b – 12	Product of Powers
= (b^2 + 4b^2) + [-2b + (-24b)] – 12	Commutative and Associative Properties
= 5b^2 + (-26b) – 12	Combine like terms.
= 5b^2 – 26b – 12	Simplify.

Example 3    Real-World EXAMPLE
CAR RENTAL Jenny pays a fee of $75 dollars to rent a car. She is charged an additional $15 for each weekday and $20 for each weekend day she uses the car. Jenny rents the car for 7 days where w of those days are weekdays. 
a. Find an equation for Jenny’s car rental bill.

WORDS	
charge | = | fee | + | number of weekdays | | 15 | + | number of weekend days | | 20.

Variables	If w = the number of weekdays she rented the car, then 7 – w = the number of weekend days she rented the car. Let C = the total charge for renting the car for the 7 days.
Equation | C | = | 75 | + | w | | 15 | + | (7 - w) | | 20
                                       C	= 75 + 15w + (7 – w)20	Write the equation. 
= 75 + 15w + 7(20) – w(20)	Distributive Property
= 75 + 15w + 140 – 20w	Simplify.
= 215 – 5w	Simplify.
An expression for Jenny’s car rental charge for 7 days is 215 – 5w, where w is the number of weekdays she rents the car.

b. Evaluate the equation to find the cost of Jenny’s car rental if 5 of the 7 days were weekdays.  
		C = 215 – 5(5)		w = 5
		    = 215 – 25		Multiply.
		    = 190			Subtract.	
Jenny’s bill is $190.	

Example 4 Polynomials on Both Sides
Solve –2(2a + 7) –2a = 4(-a – 3) + 4.
-2(2a + 7) – 2a 	= 4(-a – 3) + 4	Original equation
-4a – 14 – 2a	= -4a – 12 + 4	Distributive Property
  -6a – 14 	= -4a – 8	Combine like terms.
          -14 	= 2a – 8	Add 6a to each side.
  -6 	= 2a	Add 8 to each side.
  -3 	= a	Divide each side by 2.

The solution is –3.

Check	    -2(2a + 7) – 2a 	= 4(-a – 3) + 4	Original equation
  -2[2(-3) + 7] – 2(-3) 	= 4[-(-3) – 3] + 4	a = -3
    -2(-6 + 7) +6 	= 4(3 – 3) + 4	Simplify.
    -2(1) + 6 	= 4(0) + 4	Add and subtract.
  -2 + 6 	= 0 + 4	Multiply.
   4 	= 4  	Add.