Download Patterns, Functions and Algebra

Lesson 8-1
Multiplying Monomials
Mathematics Standards
- Number, Number Sense and Operations: Explain the
effects of operations such as multiplication or
division, and of computing powers and roots on the
magnitude of quantities.
- Patterns, Functions and Algebra: Generalize patterns
using functions or relationships and freely translate
among tabular, graphical and symbolic
representations.
- Patterns, Functions and Algebra: Describe problem
situations by using tabular, graphical and symbolic
representations.
Mathematics Standards
- Patterns, Functions and Algebra: Add, subtract,
multiply and divide monomials and polynomials.
- Patterns, Functions and Algebra: Simplify rational
expressions by eliminating common factors and
applying properties of integer exponents.
- Patterns, Functions and Algebra: Solve real-world
problems that can be modeled using linear,
quadratic, exponential or square root functions.
Vocabulary
 Monomial
Vocabulary
 Monomial - a number, a
variable, or a product of a
number and one or more
variables.
 Constant
Vocabulary
 Monomial - a number, a
variable, or a product of a
number and one or more
variables.
 Constant – A Number
Example 1
Determine whether each expression is a
monomial. Explain your reasoning.
a) 17 – s
This is not a monomial because it
involves subtraction, not multiplication.
Example 1
Determine whether each expression is a
monomial. Explain your reasoning.
b) ¾
This is a monomial because it is a real
number and an example of a constant.
Example 1
Determine whether each expression is a
monomial. Explain your reasoning.
c)
c
d
This is not a monomial because it is
the quotient, not the product, of two
variables.
Example 1
Determine whether each expression is a
monomial. Explain your reasoning.
d)
abc 8
5
 51 abc 8
This is a monomial because it is the
1
product of a number, 5 , and three
variables.
Product of Powers
Words: To multiply two
powers that have the same
base, add the exponents.
Example: a  a  a
4
12
412
or a
16
Example 2
Simplify: (6cd5)(5c5d2)
6 • c • d5 • 5 • c5 • d2
30c6d7
Power of a Power
Words: To find the power of a
power, multiply the
exponents.
Example: (k )  k
5 9
59
or k
45
Example 3
3 3 2
Simplify: [( 2 ) ]
332
2
18
2
 262,144
Power of a Product
Words: To find the power of a
product, find the power of
each factor.
Example:
 2xy 
3
  2 x y
3
3
3
or  8x y
3
3

Example 4
Simplify: 3y
5
z
 3 y
2
2
z
5 2
 9y z
10
2
2
Simplifying Monomial Expressions
To simplify an expression involving
monomials
1) each base appears exactly once,
2) there are no powers of powers, and
3) all fractions are in simplest form.
Example 5
Simplify: ( 4cd ) ( 3d )
2
2 3
 4 c d ( 3) (d )
2
2
2
3
2 3
 16c d (27)d
6
 16(27)c d d
6
2
2
2
 432c d
2
8
2
Example 6
Simplify: [(8g
h ) ] (2gh )
22 322 422
5 4
 8 g h (2gh )
4 12 16
5 4
 8 g h (2gh )
12 16
5 4
 4,096g h (2gh )
3
4 2 2
5 4
4 54
 4,096g h (2 g h )
12 16
4
 4,096g h (16g h )
12 16
 65,536g h
16
4 20
36
Homework
Pg 413
16 – 40 (even)
43 – 45 (all)