lesson 8-1 multiplying monomials. mathematics standards -number, number sense and operations:...
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Lesson 8-1Multiplying Monomials
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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.
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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.
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Vocabulary
Monomial
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Vocabulary
Monomial - a number, a variable, or a product of a number and one or more variables.
Constant
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Vocabulary
Monomial - a number, a variable, or a product of a number and one or more variables.
Constant – A Number
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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.
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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.
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Example 1
Determine whether each expression is a monomial. Explain your reasoning.
c)
This is not a monomial because it is the quotient, not the product, of two variables.
dc
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Example 1
Determine whether each expression is a monomial. Explain your reasoning.
d)
This is a monomial because it is the product of a number, , and three variables.
5
8abc
5
1
851abc
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Product of Powers
Words: To multiply two powers that have the same base, add the exponents.
Example: 16124124 or aaaa
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Example 2
Simplify: (6cd5)(5c5d2)
6 • c • d5 • 5 • c5 • d2
30c6d7
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Power of a Power
Words: To find the power of a power, multiply the exponents.
Example: 459595 or kkk )(
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Example 3
Simplify: 2332 ])[(2332
182144262,
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Power of a Product
Words: To find the power of a product, find the power of each factor.
Example: 333333 8 or 22 yxyxxy
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Example 4
Simplify: 253 zy
22523 zy
2109 zy
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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.
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Example 5
Simplify: 322 34 )()( dcd
323222 34 )()( ddc 622 2716 ddc )(6222716 ddc)(
82432 dc
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Example 6
Simplify: 452243 28 )(])[( ghhg
4522422322 28 )( ghhg 4516124 28 )( ghhg
451612 20964 )(, ghhg)(, 45441612 20964 hghg
)(, 2041612 160964 hghg361653665 hg,
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Homework
Pg 413
16 – 40 (even)
43 – 45 (all)