Download Difference of Two Squares

Name: _______________________________ Date: ___________________ Period: _____ Page: 1
Exponents and Polynomials
Expressions with Exponents/ Properties of Exponents/
Classify-Write-Add-Subtract-Multiply Polynomials
Lessons: 7-1 /7-3/7-3/7-4/7-6/7-7/7-8/7-9
Packet 7
Tennessee State Standard
SPI 3102.1.3 Apply properties to
evaluate expressions, simplify
expressions, and justify solutions to
problems.
SPI 3102.2.2 Multiply, divide, and
square numbers expressed in scientific
notation.
Common Core State Standards
A-SSE-3c Use the properties of
exponents to transform expressions for
exponential functions. For example the
expression 1.15t can be rewritten as
(1.151/12)12t ≈ 1.01212t to reveal the
approximate equivalent monthly interest
rate if the annual rate is 15%.
NRN-3 Explain why the sum or product
SPI 3102.2.3 Describe and/or order a
of two rational numbers is rational; that
given set of real numbers including both the sum of a rational number and an
rational and irrational numbers.
irrational number is irrational
SPI 3102.3.2 Operate with polynomials
and simplify results.
AAPR-1 Understand that polynomials
form a system analogous to the integers,
namely, they are closed under the
operations of addition, subtraction, and
multiplication; add, subtract, and
multiply polynomials.
Name: _______________________________ Date: ___________________ Period: _____ Page: 2
Lessons Covered 7-1 /7-2
Objective:
Skills Covered: Expressions
with Exponents/ Properties of
Exponents/Scientific Notation
Exponents and Polynomials
Name: _______________________________ Date: ___________________ Period: _____ Page: 3
Homework:
Name: _______________________________ Date: ___________________ Period: _____ Page: 4
Lessons Covered 7-1 /7-3/73/7-4
Objective:
Skills Covered: Expressions
with Exponents/ Properties of
Exponents/Scientific Notation
SCIENTIFIC NOTATION
Exponents and Polynomials
Name: _______________________________ Date: ___________________ Period: _____ Page: 5
HOMEWORK:
Name: _______________________________ Date: ___________________ Period: _____ Page: 6
Lesson 7-3 and 7-4
Multiplication and Division Properties of Exponents
Product of Powers Property
Numbers:
Algebra:
Power of a Power Property
Numbers:
Algebra:
Power of a Product Property
Numbers:
Algebra:
Quotient of Powers Property
Numbers:
Algebra:
Positive Power of a Quotient
Property
Numbers:
Algebra:
Negative Power of a Quotient
Property
Numbers:
Algebra:
Name: _______________________________ Date: ___________________ Period: _____ Page: 7
Part A. Simplify. Leave no negative or zero exponents.
1. 53 ∙ 53
2. 𝑛6 ∙ 𝑛2
3. 𝑥 2 ∙ 𝑥 −3 ∙ 𝑥 4
4. (𝑦 4 )8
5. (3−2 )2
6. (𝑎−3 )4 ∙ (𝑎7 )2
7. 𝑥𝑦 ∙ (𝑥 2 )3 ∙ (𝑦 3 )4
8. (2𝑡)5
9. (𝑎2 𝑏 2 )5
10.
2 2
13. (5)
58
11.
56
𝑥2
3
14. (𝑥𝑦3 )
22 ∙34 ∙44
29 ∙35
3 −2
15. (4)
12.
𝑎5 𝑏6
𝑎3 𝑏7
2𝑥 −4
16. (𝑦3 )
Name: _______________________________ Date: ___________________ Period: _____ Page: 8
Part B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Name: _______________________________ Date: ___________________ Period: _____ Page: 9
Lesson 7-6 and 7-7
Degrees of Polynomials/Adding & Subtracting Polynomials
Name: _______________________________ Date: ___________________ Period: _____ Page: 10
Lesson 7-6 and 7-7
Degrees of Polynomials/Adding & Subtracting Polynomials
Adding and Subtracting Polynomials
If subtraction: Rewrite
subtraction as addition of
the opposite.
Addition
Subtraction
0.9𝑦 5 − 0.4𝑦 5 + 0.5𝑥 3 + 𝑦 5
(𝑎4 − 2𝑎) − (3𝑎4 − 3𝑎 + 1)
(4𝑏 5 + 8𝑏) + (3𝑏 5 + 6𝑏 − 7𝑏 5 + 𝑏)
(3𝑥 2 − 2𝑥 + 8) − (𝑥 2 − 4)
Identify Like Terms
Draw like shapes around
like terms
Combine Like Terms:
add the coefficients
Name: _______________________________ Date: ___________________ Period: _____ Page: 11
Part A
1. Find the perimeter.
2.
3.
4.
5.
6.
7.
8.
Name: _______________________________ Date: ___________________ Period: _____ Page: 12
Part B
1. Find the perimeter:
2.
3.
4.
5.
6.
7.
8.
Name: _______________________________ Date: ___________________ Period: _____ Page: 13
Multiplying Polynomials and Special Binomials
Lesson 7-8 and 7-9
The Rectangle Method
Rules
Mono x Mono 1 x1
Mono x Binomials 1 x 2
Mono x Trinomials 1 x 3
Set up rectangle
(1st poly goes on
side/2nd goes on
top)
Multiply
coefficients
Multiply like
variables (add
exponents)
Combine Like
terms
Rules
Set up rectangle
(1st poly goes on
side/2nd goes on
top)
Multiply
coefficients
Multiply like
variables (add
exponents)
Combine Like
terms
Difference of
Two Squares
Difference of
Two Squares:
the middle term
will be 0.
Binomial x Binomial 2 x 2
Binomial x Trinomial 2 x 3
Name: _______________________________ Date: ___________________ Period: _____ Page: 14
Part A
1.
2.
3.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
4.
Name: _______________________________ Date: ___________________ Period: _____ Page: 15
Part B
1.
2.
3.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
4.
Name: _______________________________ Date: ___________________ Period: _____ Page: 16
Unit 7 Honors Page
1. 32 ∙ 3𝑥
Simplify each expression.
9. (𝑥 2 − 3𝑦 3 )2
2. (32 )𝑥
16(𝑥𝑦 2 )3 𝑧 −4
3.
4.
8𝑥 −6 (𝑦𝑧 2 )2
1
3
4
(𝑥 )
1
1
(𝑥 5 )3
1
10. What is the area of a rectangle with a length
of x - a and a width of x + b?
11. In 1867, the US purchased the Alaska
territory from Russia for $7.2 ∙ 106 . The total
area was about 6 ∙ 105 square miles. What was
the price per square mile?
1
5. (𝑎3 ) (𝑎3 ) (𝑎3 )
12. The quotient
6.
7.
5.6∙108
8∙103
is written in scientific
notation as (7 ∙ 10𝑛 ). What is the value of n?
3
√𝑎9 𝑏 3
x(4x-2)+3x(x+1)
8. (x+4)(x+4)(x-4)