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8.5 Adding and Subtracting Polynomials
* To add or subtract polynomials, combine like terms
* When subtracting polynomials, distribute -1 first
Examples:
(
)(
1. 4 p 2 + 5 p + 2 p 2 + p
)
(
3. ( 8 cd 3d + 4 c ) + ( 6 c + 2 cd )
(
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8.6 Multiplying a Polynomial by a Monomial
* Use the distributive property to multiply a monomial and a polynomial *
Remember to add exponents when multiplying variables
Examples: Find each product.
(
1. 3y ( 5 y + 2 )
2. 9b 2 2b
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8.7 Multiplying Polynomials
To multiply two binomials, use the FOIL method by multiplying the.
First terms
Outer terms
Inner terms
Last terms
Examples: Find each product.
1. ( y + 4 ) ( y + 3)
2. ( x 2 ) ( x + 6 )
3. ( a 8 ) ( a
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8.8 Special Products
Any binomials can be multiplied using FOIL, however some cases follow special patterns.
The patterns allow you to multiply some polynomials quickly.
Square of a Sum: ( a + b ) = a 2 + 2 ab + b 2
2
Square of a
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8.1 Multiplying Monomials
Monomial: _
_
abc 3
Examples: 7, x , 189 y ,
4
Examples: Determine whether each expression is a monomial. Write yes or no.
4a
1. 5 7 a
2.
3. n
3b
4. x 2 y
Rules for Multiplying Monomials
Rule
Notation
am
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8.2 Dividing Monomials
Rules for Dividing Monomials
Rule
Notation
am
= a mn
an
To divide powers that have the same
base, subtract the exponents.
Example
b15
= b15 7 = b 8
b7
To find the power of a quotient, find the
power of the
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8.3 Scientific Notation
A number in scientific notation is written as a 10 n where 1 a < 10 and n is an integer.
Converting Numbers from Scientific to Standard Notation
* If n is a positive number, move the decimal n places to th
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8.4 Polynomials
Polynomial:
Examples: 7, 8y, y + z + w 2 , x 7 , x 4 + 8 x 3 2 x 2 + 32
Binomial:
Examples: x 7 , 3y + 2 x
Trinomial:
Examples: x 2 + x + 5 , y + z + w 2
Examples Determine whether each polynomial is a monomial, b