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5.3 Multiplying and Dividing
Monomials
• Goals: To multiply and divide monomials
Monomial:
• An expression that is either a:
(1) numeral or constant, ex : 5
(2)a variable, ex: x
(3)or a product of numerals and variables ex: 5x
(4)variables with whole number exponents. Ex: x²
• If the monomial is a numeral, it is called a constant.
• Excludes: “+”, “-”, and if exponent is negative or a
fraction.
4x3
x3 + 4
-8
2x2y
1
y

7
ab
1
x
2
1 5
y
2
Multiply 2 monomials using “properties”
(3x • 4x) = (3 • 4)(x • x) = 12x2
(Associative and Commutative) Group the
numbers together and then group the same
variables together
(3x2)(-x) = (3x2)(-1x) = (3 • -1)(x2 •x)
= -3x3
(-7x2y5)(4xy3)
(-7 • 4)(x2 • x)(y5 • y3)
-28x3 y8
Multiply:
2
(7y)(2y )
=
3
14y
Multiply:
-2
7
(5y )(3y )
=
5
15y
Multiply:
3
5
(-3y )(4xy )
=
8
-12xy
Divide monomials using properties:
Group the numbers together and either divide
or reduce and then group the like bases
together.
5
x
52
3

x

x
2
x
2
27
4x
4x

7
5x
5
4

5
5x
Divide monomials using properties:
5 12
8x y
8
53
1210


x

y
3 10
 2x y
2
 4 x y
2
2
Solve:
5
12m
3

3
m
8
4m
3
 3
m
Solve:
1 118
9m

m
8
27 m
3
11
3
m

3
Solve:
 5x y
2
 5x y
3
4
 xy
3
Solve:
 32 x y
14 6
8x y
15
7
 4 xy
Assignment:
Page 215
(4-66 even)
52) m
Show this step:
 m  m m   m
2 4
3 2
8
6
14