Text 8. Polynomials
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ALGEBRA PROJECT UNIT 8 POLYNOMIALS
POLYNOMIALS
Lesson 1
Multiplying Monomials
Lesson 2
Dividing Monomials
Lesson 3
Scientific Notation
Lesson 4
Polynomials
Lesson 5
Adding and Subtracting Polynomials
Lesson 6
Multiplying Polynomials by a Monomial
Lesson 7
Multiplying Polynomials
Lesson 8
Special Products
MULTIPLY MONOMIALS
Example 1
Identify Monomials
Example 2
Product of Powers
Example 3
Power of a Power
Example 4
Power of a Product
Example 5
Simplify Expressions
Determine whether each expression is a monomial. Explain your reasoning. Expression
Monomial?
a.
no
b.
yes
c.
yes
Reason The expression involves subtraction, not the product, of two variables. The expression is the product of a number and two variables. is a real number and an example of a constant.
d.
xy
yes
The expression is the product of two variables.
Determine whether each expression is a monomial. Explain your reasoning. Expression
Monomial?
Reason
yes
Single variables are monomials.
b.
no
The expression involves subtraction, not the product, of two variables.
c.
no
The expression is the quotient, not the product, of two variables.
a.
The expression is the product of a d.
yes
number,
, and two variables.
Simplify
. Commutative and Associative Properties Product of Powers
Answer:
Simplify.
Simplify
. Communicative and Associative Properties Product of Powers
Answer:
Simplify.
Simplify each expression. a.
Answer:
b.
Answer:
Simplify Power of a Power Simplify. Power of a Power Answer:
Simplify.
Simplify Answer:
Geometry Find the volume of a cube with a side length Volume
Formula for volume of a cube
Power of a Product Answer:
Simplify.
Express the surface area of the cube as a monomial. Answer:
Simplify
Power of a Power Power of a Product Power of a Power
Commutative Property
Answer:
Power of Powers
Simplify Answer:
DIVIDING MONOMIALS
Example 1
Quotient of Powers
Example 2
Power of a Quotient
Example 3
Zero Exponent
Example 4
Negative Exponents
Example 5
Apply Properties of Exponents
Simplify
Assume that x and y are not equal
to zero. Group powers that have the same base. Quotient of Powers Answer:
Simplify.
Simplify to zero. Answer:
Assume that a and b are not equal
Simplify
Assume that e and f are not
equal to zero. Power of a Quotient
Power of a Product
Answer:
Power of a Power
Simplify equal to zero.
Answer:
Assume that p and q are not
Simplify equal to zero.
Answer: 1
Assume that m and n are not
Simplify
. Assume that m and n are not
equal to zero.
Simplify. Answer:
Quotient of Powers
Simplify each expression. Assume that z is not equal to zero. a.
Answer: 1
b.
Answer:
Simplify
. Assume that y and z are not
equal to zero. Write as a product of fractions.
Answer:
Multiply fractions.
Simplify
. Assume that p, q, and r are
not equal to zero. Group powers with the same base. Quotient of Powers and Negative Exponent Properties
Simplify.
Negative Exponent Property Answer:
Multiply fractions.
Simplify each expression. Assume that no denominator is equal to zero. a.
Answer:
b.
Answer:
Multiple-Choice Test Item Write the ratio of the circumference of the circle to the area of the square in simplest form. A
B
C
D
Read the Test Item A ratio is a comparison of two quantities. It can be written in fraction form.
Solve the Test Item •
•
circumference of a circle length of a square diameter of circle or 2r area of square Substitute. Quotient of Powers
Simplify.
Answer: C
Multiple-Choice Test Item Write the ratio of the circumference of the circle to the perimeter of the square in simplest form. A
B
Answer: A
C
D
SCIENTIFIC NOTATION
Example 1
Scientific to Standard Notation
Example 2
Standard to Scientific Notation
Example 3
Use Scientific Notation
Example 4
Multiplication with Scientific Notation
Example 5
Division with Scientific Notation
Express
in standard notation. move decimal point 3 places to the left.
Answer: 0.00748
Express
in standard notation. move decimal point 5 places to the right.
Answer: 219,000
Express each number in standard notation. a.
Answer: 0.0316
b.
Answer: 7610
Express 0.000000672 in scientific notation. Move decimal point 7 places to the right. and
Answer:
Express 3,022,000,000,000 in scientific notation.
Move decimal point 12 places to the left. and
Answer:
Express each number in scientific notation. a.
458,000,000
Answer:
b.
0.0000452
Answer:
The Sporting Goods Manufacturers Association reported that in 2000, women spent $4.4 billion on 124 million pairs of shoes. Men spent $8.3 billion on 169 million pairs of shoes. Express the numbers of pairs of shoes sold to women, pairs sold to men, and total spent by both men and women in standard notation. Answer: Shoes sold to women: Shoes sold to men: Total spent:
Write each of these numbers in scientific notation. Answer: Shoes sold to women: Shoes sold to men: Total spent:
The average circulation for all U.S. daily newspapers in 2000 was 111.5 billion newspapers. The top three leading newspapers were The Wall Street Journal, with a circulation of 1.76 million newspapers, USA Today, which sold 1.69 million newspapers, and The New York Times, which had 1.10 million readers. a.
Express the average daily circulation and the circulation of the top three newspapers in standard notation.
Answer: Total circulation: 111,500,000,000; The Wall Street Journal: 1,760,000; USA Today: 1,690,000; The New York Times: 1,100,000
The average circulation for all U.S. daily newspapers in 2000 was 111.5 billion newspapers. The top three leading newspapers were The Wall Street Journal, with a circulation of 1.76 million newspapers, USA Today, which sold 1.69 million newspapers, and The New York Times, which had 1.10 million readers. b. Write each of the numbers in scientific notation. Answer: Total circulation: Journal: USA Today: The New York Times:
The Wall Street
Evaluate Express the result in scientific and standard notation.
Commutative and Associative Properties Product of Powers
Associative Property
Product of Powers Answer:
Evaluate Express the result in scientific and standard notation. Answer:
Evaluate
Express the result in scientific
and standard notation.
Associative Property
Product of Powers Answer:
Evaluate and standard notation. Answer:
Express the result in scientific
POLYNOMIALS
Example 1
Identify Polynomials
Example 2
Write a Polynomial
Example 3
Degree of a Polynomial
Example 4
Arrange Polynomials in Ascending Order
Example 5
Arrange Polynomials in Descending Order
State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. Expression
a. b . c. d .
Polynomial? Yes, is the difference of two real numbers.
Monomial, Binomial, or Trinomial binomial
Yes, is the sum and difference of trinomial three monomials. No. Yes,
are not monomials. has one term.
none of these monomial
State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. Expression
a.
Polynomial? Yes, is the sum of three monomials. which is not a monomial.
Monomial, Binomial, or Trinomial trinomial
b . c.
No.
Yes, The expression is the sum of two monomials.
binomial
d .
Yes,
monomial
has one term.
none of these
Write a polynomial to represent the area of the green shaded region. Words
The area of the shaded region is the area of the rectangle minus the area of the triangle.
Variables
area of the shaded region height of rectangle area of rectangle triangle area
Equation
A A
Answer: The polynomial representing the area of the shaded region is
Write a polynomial to represent the area of the green shaded region.
Answer:
Find the degree of each polynomial. Degree of Each Term
Degree of Polynomial
a.
0, 1, 2, 3
3
b.
2, 1, 0
2
c.
8
8
Polynomial
Terms
Find the degree of each polynomial. Degree of Each Term
Degree of Polynomial
a.
2, 1, 3, 0
3
b.
2, 4, 3
4
c.
7, 6
7
Polynomial
Terms
Arrange the terms of powers of x are in ascending order.
Answer:
so that the
Arrange the terms of the powers of x are in ascending order.
Answer:
so that
Arrange the terms of each polynomial so that the powers of x are in ascending order. a. Answer:
b. Answer:
Arrange the terms of the powers of x are in descending order.
Answer:
so that
Arrange the terms of that the powers of x are in descending order.
Answer:
so
Arrange the terms of each polynomial so that the powers of x are in descending order. a. Answer:
b. Answer:
ADDING AND SUBTRACTING POLYNOMIALS
Example 1
Add Polynomials
Example 2
Subtract Polynomials
Example 3
Subtract Polynomials
Find Method 1 Horizontal Group like terms together.
Associative and Commutative Properties Add like terms.
Method 2 Vertical Align the like terms in columns and add. Notice that terms are in descending order with like terms aligned.
Answer:
Find Answer:
Find Method 1 Horizontal Subtract
by adding its additive inverse.
The additive inverse of is Group like terms. Add like terms.
Method 2 Vertical Align like terms in columns and subtract by adding the additive inverse.
Add the opposite.
Answer:
or
Find Answer:
Geometry The measure of the perimeter of the triangle shown is Find the polynomial that represents the third side of the triangle. Let a = length of side 1, b = the length of side 2, and c = the length of the third side. You can find a polynomial for the third side by subtracting side a and side b from the polynomial for the perimeter.
To subtract, add the additive inverses.
Group the like terms. Add like terms. Answer: The polynomial for the third side is
Find the length of the third side if the triangle if
The length of the third side is
Simplify. Answer: 45 units
Geometry The measure of the perimeter of the rectangle shown is
a. Find a polynomial that represents width of the rectangle. Answer: b. Find the width of the rectangle if Answer: 3 units
MULTIPLYING POLYNOMIALS by a MONOMIAL
Example 1
Multiply a Polynomial by a Monomial
Example 2
Simplify Expressions
Example 3
Use Polynomial Models
Example 4
Polynomials on Both Sides
Find Method 1 Horizontal
Distributive Property Multiply.
Find Method 2 Vertical
Distributive Property Multiply.
Answer:
Find Answer:
Simplify
Distributive Property Product of Powers Commutative and Associative Properties
Answer:
Combine like terms.
Simplify
Answer:
Entertainment Admission to the Super Fun Amusement Park is $10. Once in the park, super rides are an additional $3 each and regular rides are an additional $2. Sarita goes to the park and rides 15 rides, of which s of those 15 are super rides. Find an expression for how much money Sarita spent at the park. Words Variables
The total cost is the sum of the admission, super ride costs, and regular ride costs. If the number of super rides, then is the number of regular rides. Let M be the amount of money Sarita spent at the park.
Equation Amount of money
M
equals
admission
10
plus
super rides
s
$3 per times ride
regular plus rides
times
$2 per ride.
2
3
Distributive Property Simplify Simplify. Answer: An expression for the amount of money Sarita spent in the park is , where s is the number of super rides she rode.
Evaluate the expression to find the cost if Sarita rode 9 super rides.
Add. Answer: Sarita spent $49.
The Fosters own a vacation home that they rent throughout the year. The rental rate during peak season is $120 per day and the rate during the off-peak season is $70 per day. Last year they rented the house 210 days, p of which were during peak season. a.
Find an expression for how much rent the Fosters received.
Answer: b.
Evaluate the expression if p is equal to 130.
Answer: $21,200
Solve Original equation Distributive Property Combine like terms. Subtract each side.
from
Add 7 to each side. Add 2b to each side. Divide each side by 14. Answer:
Check
Original equation
Simplify. Multiply. Add and subtract.
Solve Answer:
MULTIPLY POLYNOMIALS
Example 1
The Distributive Property
Example 2
FOIL Method
Example 3
FOIL Method
Example 4
The Distributive Property
Find Method 1 Vertical Multiply by –4.
Find Multiply by y.
Find Add like terms.
Find Method 2 Horizontal Distributive Property Distributive Property Multiply. Combine like terms. Answer:
Find Answer:
Find F
L
I O
F
O
I
L
Multiply. Combine like terms.
Answer:
Find
F
O
I
L
Multiply.
Answer:
Combine like terms.
Find each product. a. Answer:
b. Answer:
Geometry The area A of a triangle is one-half the height h times the base b. Write an expression for the area of the triangle. Identify the height and the base.
Now write and apply the formula. Area
A
equals
one-half
height
h
times
base.
b
Original formula
Substitution
FOIL method
Multiply.
Combine like terms.
Distributive Property Answer: The area of the triangle is square units.
Geometry The area of a rectangle is the measure of the base times the height. Write an expression for the area of the rectangle. Answer:
Find
Distributive Property Distributive Property Answer:
Combine like terms.
Find
Distributive Property
Distributive Property Answer: Combine like terms.
Find each product. a. Answer: b. Answer:
SPECIAL PRODUCTS
Example 1
Square of a Sum
Example 2
Square of a Difference
Example 3
Apply the Sum of a Square
Example 4
Product of a Sum and a Difference
Find Square of a Sum
Answer:
Simplify.
Check
Check your work by using the FOIL method.
F
O
I
L
Find Square of a Sum
Answer:
Simplify.
Find each product. a. Answer: b. Answer:
Find Square of a Difference
Answer:
Simplify.
Find Square of a Difference
Answer:
Simplify.
Find each product. a. Answer: b. Answer:
Geometry Write an expression that represents the area of a square that has a side length of units. The formula for the area of a square is Area of a square
Simplify. Answer: The area of the square is square units.
Geometry Write an expression that represents the area of a square that has a side length of units. Answer:
Find Product of a Sum and a Difference
Answer:
Simplify.
Find
Product of a Sum and a Difference
Answer: Simplify.
Find each product. a. Answer: b. Answer:
THIS IS THE END OF THE SESSION
BYE!
POLYNOMIALS
Lesson 1
Multiplying Monomials
Lesson 2
Dividing Monomials
Lesson 3
Scientific Notation
Lesson 4
Polynomials
Lesson 5
Adding and Subtracting Polynomials
Lesson 6
Multiplying Polynomials by a Monomial
Lesson 7
Multiplying Polynomials
Lesson 8
Special Products
MULTIPLY MONOMIALS
Example 1
Identify Monomials
Example 2
Product of Powers
Example 3
Power of a Power
Example 4
Power of a Product
Example 5
Simplify Expressions
Determine whether each expression is a monomial. Explain your reasoning. Expression
Monomial?
a.
no
b.
yes
c.
yes
Reason The expression involves subtraction, not the product, of two variables. The expression is the product of a number and two variables. is a real number and an example of a constant.
d.
xy
yes
The expression is the product of two variables.
Determine whether each expression is a monomial. Explain your reasoning. Expression
Monomial?
Reason
yes
Single variables are monomials.
b.
no
The expression involves subtraction, not the product, of two variables.
c.
no
The expression is the quotient, not the product, of two variables.
a.
The expression is the product of a d.
yes
number,
, and two variables.
Simplify
. Commutative and Associative Properties Product of Powers
Answer:
Simplify.
Simplify
. Communicative and Associative Properties Product of Powers
Answer:
Simplify.
Simplify each expression. a.
Answer:
b.
Answer:
Simplify Power of a Power Simplify. Power of a Power Answer:
Simplify.
Simplify Answer:
Geometry Find the volume of a cube with a side length Volume
Formula for volume of a cube
Power of a Product Answer:
Simplify.
Express the surface area of the cube as a monomial. Answer:
Simplify
Power of a Power Power of a Product Power of a Power
Commutative Property
Answer:
Power of Powers
Simplify Answer:
DIVIDING MONOMIALS
Example 1
Quotient of Powers
Example 2
Power of a Quotient
Example 3
Zero Exponent
Example 4
Negative Exponents
Example 5
Apply Properties of Exponents
Simplify
Assume that x and y are not equal
to zero. Group powers that have the same base. Quotient of Powers Answer:
Simplify.
Simplify to zero. Answer:
Assume that a and b are not equal
Simplify
Assume that e and f are not
equal to zero. Power of a Quotient
Power of a Product
Answer:
Power of a Power
Simplify equal to zero.
Answer:
Assume that p and q are not
Simplify equal to zero.
Answer: 1
Assume that m and n are not
Simplify
. Assume that m and n are not
equal to zero.
Simplify. Answer:
Quotient of Powers
Simplify each expression. Assume that z is not equal to zero. a.
Answer: 1
b.
Answer:
Simplify
. Assume that y and z are not
equal to zero. Write as a product of fractions.
Answer:
Multiply fractions.
Simplify
. Assume that p, q, and r are
not equal to zero. Group powers with the same base. Quotient of Powers and Negative Exponent Properties
Simplify.
Negative Exponent Property Answer:
Multiply fractions.
Simplify each expression. Assume that no denominator is equal to zero. a.
Answer:
b.
Answer:
Multiple-Choice Test Item Write the ratio of the circumference of the circle to the area of the square in simplest form. A
B
C
D
Read the Test Item A ratio is a comparison of two quantities. It can be written in fraction form.
Solve the Test Item •
•
circumference of a circle length of a square diameter of circle or 2r area of square Substitute. Quotient of Powers
Simplify.
Answer: C
Multiple-Choice Test Item Write the ratio of the circumference of the circle to the perimeter of the square in simplest form. A
B
Answer: A
C
D
SCIENTIFIC NOTATION
Example 1
Scientific to Standard Notation
Example 2
Standard to Scientific Notation
Example 3
Use Scientific Notation
Example 4
Multiplication with Scientific Notation
Example 5
Division with Scientific Notation
Express
in standard notation. move decimal point 3 places to the left.
Answer: 0.00748
Express
in standard notation. move decimal point 5 places to the right.
Answer: 219,000
Express each number in standard notation. a.
Answer: 0.0316
b.
Answer: 7610
Express 0.000000672 in scientific notation. Move decimal point 7 places to the right. and
Answer:
Express 3,022,000,000,000 in scientific notation.
Move decimal point 12 places to the left. and
Answer:
Express each number in scientific notation. a.
458,000,000
Answer:
b.
0.0000452
Answer:
The Sporting Goods Manufacturers Association reported that in 2000, women spent $4.4 billion on 124 million pairs of shoes. Men spent $8.3 billion on 169 million pairs of shoes. Express the numbers of pairs of shoes sold to women, pairs sold to men, and total spent by both men and women in standard notation. Answer: Shoes sold to women: Shoes sold to men: Total spent:
Write each of these numbers in scientific notation. Answer: Shoes sold to women: Shoes sold to men: Total spent:
The average circulation for all U.S. daily newspapers in 2000 was 111.5 billion newspapers. The top three leading newspapers were The Wall Street Journal, with a circulation of 1.76 million newspapers, USA Today, which sold 1.69 million newspapers, and The New York Times, which had 1.10 million readers. a.
Express the average daily circulation and the circulation of the top three newspapers in standard notation.
Answer: Total circulation: 111,500,000,000; The Wall Street Journal: 1,760,000; USA Today: 1,690,000; The New York Times: 1,100,000
The average circulation for all U.S. daily newspapers in 2000 was 111.5 billion newspapers. The top three leading newspapers were The Wall Street Journal, with a circulation of 1.76 million newspapers, USA Today, which sold 1.69 million newspapers, and The New York Times, which had 1.10 million readers. b. Write each of the numbers in scientific notation. Answer: Total circulation: Journal: USA Today: The New York Times:
The Wall Street
Evaluate Express the result in scientific and standard notation.
Commutative and Associative Properties Product of Powers
Associative Property
Product of Powers Answer:
Evaluate Express the result in scientific and standard notation. Answer:
Evaluate
Express the result in scientific
and standard notation.
Associative Property
Product of Powers Answer:
Evaluate and standard notation. Answer:
Express the result in scientific
POLYNOMIALS
Example 1
Identify Polynomials
Example 2
Write a Polynomial
Example 3
Degree of a Polynomial
Example 4
Arrange Polynomials in Ascending Order
Example 5
Arrange Polynomials in Descending Order
State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. Expression
a. b . c. d .
Polynomial? Yes, is the difference of two real numbers.
Monomial, Binomial, or Trinomial binomial
Yes, is the sum and difference of trinomial three monomials. No. Yes,
are not monomials. has one term.
none of these monomial
State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. Expression
a.
Polynomial? Yes, is the sum of three monomials. which is not a monomial.
Monomial, Binomial, or Trinomial trinomial
b . c.
No.
Yes, The expression is the sum of two monomials.
binomial
d .
Yes,
monomial
has one term.
none of these
Write a polynomial to represent the area of the green shaded region. Words
The area of the shaded region is the area of the rectangle minus the area of the triangle.
Variables
area of the shaded region height of rectangle area of rectangle triangle area
Equation
A A
Answer: The polynomial representing the area of the shaded region is
Write a polynomial to represent the area of the green shaded region.
Answer:
Find the degree of each polynomial. Degree of Each Term
Degree of Polynomial
a.
0, 1, 2, 3
3
b.
2, 1, 0
2
c.
8
8
Polynomial
Terms
Find the degree of each polynomial. Degree of Each Term
Degree of Polynomial
a.
2, 1, 3, 0
3
b.
2, 4, 3
4
c.
7, 6
7
Polynomial
Terms
Arrange the terms of powers of x are in ascending order.
Answer:
so that the
Arrange the terms of the powers of x are in ascending order.
Answer:
so that
Arrange the terms of each polynomial so that the powers of x are in ascending order. a. Answer:
b. Answer:
Arrange the terms of the powers of x are in descending order.
Answer:
so that
Arrange the terms of that the powers of x are in descending order.
Answer:
so
Arrange the terms of each polynomial so that the powers of x are in descending order. a. Answer:
b. Answer:
ADDING AND SUBTRACTING POLYNOMIALS
Example 1
Add Polynomials
Example 2
Subtract Polynomials
Example 3
Subtract Polynomials
Find Method 1 Horizontal Group like terms together.
Associative and Commutative Properties Add like terms.
Method 2 Vertical Align the like terms in columns and add. Notice that terms are in descending order with like terms aligned.
Answer:
Find Answer:
Find Method 1 Horizontal Subtract
by adding its additive inverse.
The additive inverse of is Group like terms. Add like terms.
Method 2 Vertical Align like terms in columns and subtract by adding the additive inverse.
Add the opposite.
Answer:
or
Find Answer:
Geometry The measure of the perimeter of the triangle shown is Find the polynomial that represents the third side of the triangle. Let a = length of side 1, b = the length of side 2, and c = the length of the third side. You can find a polynomial for the third side by subtracting side a and side b from the polynomial for the perimeter.
To subtract, add the additive inverses.
Group the like terms. Add like terms. Answer: The polynomial for the third side is
Find the length of the third side if the triangle if
The length of the third side is
Simplify. Answer: 45 units
Geometry The measure of the perimeter of the rectangle shown is
a. Find a polynomial that represents width of the rectangle. Answer: b. Find the width of the rectangle if Answer: 3 units
MULTIPLYING POLYNOMIALS by a MONOMIAL
Example 1
Multiply a Polynomial by a Monomial
Example 2
Simplify Expressions
Example 3
Use Polynomial Models
Example 4
Polynomials on Both Sides
Find Method 1 Horizontal
Distributive Property Multiply.
Find Method 2 Vertical
Distributive Property Multiply.
Answer:
Find Answer:
Simplify
Distributive Property Product of Powers Commutative and Associative Properties
Answer:
Combine like terms.
Simplify
Answer:
Entertainment Admission to the Super Fun Amusement Park is $10. Once in the park, super rides are an additional $3 each and regular rides are an additional $2. Sarita goes to the park and rides 15 rides, of which s of those 15 are super rides. Find an expression for how much money Sarita spent at the park. Words Variables
The total cost is the sum of the admission, super ride costs, and regular ride costs. If the number of super rides, then is the number of regular rides. Let M be the amount of money Sarita spent at the park.
Equation Amount of money
M
equals
admission
10
plus
super rides
s
$3 per times ride
regular plus rides
times
$2 per ride.
2
3
Distributive Property Simplify Simplify. Answer: An expression for the amount of money Sarita spent in the park is , where s is the number of super rides she rode.
Evaluate the expression to find the cost if Sarita rode 9 super rides.
Add. Answer: Sarita spent $49.
The Fosters own a vacation home that they rent throughout the year. The rental rate during peak season is $120 per day and the rate during the off-peak season is $70 per day. Last year they rented the house 210 days, p of which were during peak season. a.
Find an expression for how much rent the Fosters received.
Answer: b.
Evaluate the expression if p is equal to 130.
Answer: $21,200
Solve Original equation Distributive Property Combine like terms. Subtract each side.
from
Add 7 to each side. Add 2b to each side. Divide each side by 14. Answer:
Check
Original equation
Simplify. Multiply. Add and subtract.
Solve Answer:
MULTIPLY POLYNOMIALS
Example 1
The Distributive Property
Example 2
FOIL Method
Example 3
FOIL Method
Example 4
The Distributive Property
Find Method 1 Vertical Multiply by –4.
Find Multiply by y.
Find Add like terms.
Find Method 2 Horizontal Distributive Property Distributive Property Multiply. Combine like terms. Answer:
Find Answer:
Find F
L
I O
F
O
I
L
Multiply. Combine like terms.
Answer:
Find
F
O
I
L
Multiply.
Answer:
Combine like terms.
Find each product. a. Answer:
b. Answer:
Geometry The area A of a triangle is one-half the height h times the base b. Write an expression for the area of the triangle. Identify the height and the base.
Now write and apply the formula. Area
A
equals
one-half
height
h
times
base.
b
Original formula
Substitution
FOIL method
Multiply.
Combine like terms.
Distributive Property Answer: The area of the triangle is square units.
Geometry The area of a rectangle is the measure of the base times the height. Write an expression for the area of the rectangle. Answer:
Find
Distributive Property Distributive Property Answer:
Combine like terms.
Find
Distributive Property
Distributive Property Answer: Combine like terms.
Find each product. a. Answer: b. Answer:
SPECIAL PRODUCTS
Example 1
Square of a Sum
Example 2
Square of a Difference
Example 3
Apply the Sum of a Square
Example 4
Product of a Sum and a Difference
Find Square of a Sum
Answer:
Simplify.
Check
Check your work by using the FOIL method.
F
O
I
L
Find Square of a Sum
Answer:
Simplify.
Find each product. a. Answer: b. Answer:
Find Square of a Difference
Answer:
Simplify.
Find Square of a Difference
Answer:
Simplify.
Find each product. a. Answer: b. Answer:
Geometry Write an expression that represents the area of a square that has a side length of units. The formula for the area of a square is Area of a square
Simplify. Answer: The area of the square is square units.
Geometry Write an expression that represents the area of a square that has a side length of units. Answer:
Find Product of a Sum and a Difference
Answer:
Simplify.
Find
Product of a Sum and a Difference
Answer: Simplify.
Find each product. a. Answer: b. Answer:
THIS IS THE END OF THE SESSION
BYE!
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