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How to Add and Subtract Polynomials: Easy Steps and Examples

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How to Add and Subtract Polynomials: Easy Steps and Examples
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Mahak Tiwari

@mahaktiwari_ikmn

·

70 Followers

Follow

This lesson covers adding polynomials and subtracting polynomials, as well as multiplying monomials. It explains key concepts like monomials, polynomials, degree of polynomials, and provides step-by-step examples for adding and subtracting polynomials using both vertical and horizontal formats.

• Monomials are defined as numbers, variables, or products of numbers and variables
• Polynomials are expressions made up of monomial terms
• The degree of a polynomial is determined by the highest exponent
• Adding and subtracting polynomials involves combining like terms
• Vertical and horizontal formats can be used for polynomial operations
• Subtracting polynomials is done by adding the opposite

2/17/2023

399

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

More Practice Problems and Introduction to Multiplication of Monomials

This page continues with additional practice problems on adding polynomials and subtracting polynomials, followed by an introduction to the multiplication of monomials.

The practice problems reinforce the concepts and techniques covered in previous sections, with a mix of addition and subtraction problems involving polynomials of various degrees and with multiple variables.

Example: (4y³-y-1)-(2y²-3y+3) = 4y³-2y²+2y-4

The introduction to multiplication of monomials begins by reviewing key concepts:

  1. In exponential expressions, the base and exponent are identified.
  2. The exponent indicates the number of times the base occurs as a factor.

Definition: The product of exponential expressions with the same base can be simplified by writing each expression in factored form and combining the exponents.

This introduction sets the stage for more detailed exploration of monomial multiplication in subsequent sections.

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

Subtracting Polynomials

This page covers techniques for subtracting polynomials using both vertical and horizontal formats.

The key principle introduced is that subtracting polynomials is equivalent to adding the opposite of the second polynomial to the first. Two detailed examples illustrate this process:

Example 3 demonstrates subtracting polynomials using a vertical format: (-3x+7) - (8x²+3x-4)

The solution shows how to:

  1. Find the opposite of the second polynomial
  2. Arrange terms in descending order
  3. Align like terms in columns
  4. Combine terms in each column

Example 4 illustrates subtracting polynomials using a horizontal format: (5x²-3x+4)-(-3x³-2x+8)

This example demonstrates:

  1. Rewriting subtraction as addition of the opposite
  2. Rearranging and grouping like terms
  3. Combining like terms
  4. Writing the final polynomial in descending order

Highlight: When subtracting polynomials, remember to add the opposite of the second polynomial. This effectively turns subtraction into addition.

The page includes several practice problems for adding and subtracting polynomials, providing students with opportunities to apply these techniques.

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

Practice Problems: Adding and Subtracting Polynomials

This page contains a series of practice problems focused on adding polynomials and subtracting polynomials. The problems cover various scenarios, including:

  1. Adding polynomials with different degrees
  2. Adding polynomials with multiple variables
  3. Subtracting polynomials
  4. Combining addition and subtraction of polynomials

Each problem is presented with a step-by-step solution, reinforcing the techniques learned in the previous sections. The solutions demonstrate:

  • Proper alignment of like terms
  • Combining like terms
  • Writing polynomials in descending order

Example: (2a²-7a+10) + (a²+4a-7) = 3a²-3a+3

These practice problems provide valuable opportunities for students to apply their understanding of polynomial operations and gain confidence in their skills.

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

Introduction to Polynomials

This page introduces key concepts related to polynomials and monomials.

A monomial is defined as a number, variable, or product of numbers and variables. Examples are provided to illustrate different types of monomials, such as 7 (a number), b (a variable), and 12xy² (a product of a number and variables).

The text then defines a polynomial as a variable expression made up of monomial terms. It explains that polynomials can be classified based on the number of terms:

  • A monomial is a polynomial with one term
  • A binomial has two terms
  • A trinomial contains three terms

Example: 7x² is a monomial, 4x+2 is a binomial, and 7x²+5x-7 is a trinomial.

The concept of descending order for polynomials is introduced, where terms are arranged so the exponents on the variable decrease from left to right.

Definition: The degree of a polynomial in one variable is the value of the largest exponent on the variable.

Example: The degree of 4x³-3x²+6x-1 is 3.

The page concludes with some additional notes on polynomial degree:

  • The degree of a nonzero constant is zero
  • Zero has no degree
HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

Adding Polynomials

This page focuses on techniques for adding polynomials using both vertical and horizontal formats.

The key principle emphasized is combining like terms when adding polynomials. Two detailed examples are provided to illustrate the process:

Example 1 demonstrates adding polynomials using a vertical format: (2x²+x-1) + (3x³ + 4x²-5)

The solution shows how to:

  1. Arrange terms in descending order
  2. Align like terms in columns
  3. Combine terms in each column

Example 2 shows adding polynomials horizontally: (3x³-7x+2)+(7x²+2x-7)

This example illustrates:

  1. Using commutative and associative properties to rearrange terms
  2. Grouping like terms
  3. Combining like terms
  4. Writing the final polynomial in descending order

Highlight: When adding polynomials, the key is to identify and combine like terms, regardless of whether you use a vertical or horizontal format.

The page also introduces the concept of the opposite of a polynomial, where the sign of every term is changed. This is important for the subtraction of polynomials, which is introduced next.

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

View

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SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

/

Algebra 1

/

Binomials & polynomials

/

Special products of binomials

How to Add and Subtract Polynomials: Easy Steps and Examples

user profile picture

Mahak Tiwari

@mahaktiwari_ikmn

·

70 Followers

Follow

This lesson covers adding polynomials and subtracting polynomials, as well as multiplying monomials. It explains key concepts like monomials, polynomials, degree of polynomials, and provides step-by-step examples for adding and subtracting polynomials using both vertical and horizontal formats.

• Monomials are defined as numbers, variables, or products of numbers and variables
• Polynomials are expressions made up of monomial terms
• The degree of a polynomial is determined by the highest exponent
• Adding and subtracting polynomials involves combining like terms
• Vertical and horizontal formats can be used for polynomial operations
• Subtracting polynomials is done by adding the opposite

2/17/2023

399

 

Algebra 1

15

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

Free Study Notes from Top Students - Unlock Now!

Free notes for every subject, made by the best students

Get better grades with smart AI support

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More Practice Problems and Introduction to Multiplication of Monomials

This page continues with additional practice problems on adding polynomials and subtracting polynomials, followed by an introduction to the multiplication of monomials.

The practice problems reinforce the concepts and techniques covered in previous sections, with a mix of addition and subtraction problems involving polynomials of various degrees and with multiple variables.

Example: (4y³-y-1)-(2y²-3y+3) = 4y³-2y²+2y-4

The introduction to multiplication of monomials begins by reviewing key concepts:

  1. In exponential expressions, the base and exponent are identified.
  2. The exponent indicates the number of times the base occurs as a factor.

Definition: The product of exponential expressions with the same base can be simplified by writing each expression in factored form and combining the exponents.

This introduction sets the stage for more detailed exploration of monomial multiplication in subsequent sections.

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

Free Study Notes from Top Students - Unlock Now!

Free notes for every subject, made by the best students

Get better grades with smart AI support

Study smarter, stress less - anytime, anywhere

Sign up with Email

By signing up you accept Terms of Service and Privacy Policy

Subtracting Polynomials

This page covers techniques for subtracting polynomials using both vertical and horizontal formats.

The key principle introduced is that subtracting polynomials is equivalent to adding the opposite of the second polynomial to the first. Two detailed examples illustrate this process:

Example 3 demonstrates subtracting polynomials using a vertical format: (-3x+7) - (8x²+3x-4)

The solution shows how to:

  1. Find the opposite of the second polynomial
  2. Arrange terms in descending order
  3. Align like terms in columns
  4. Combine terms in each column

Example 4 illustrates subtracting polynomials using a horizontal format: (5x²-3x+4)-(-3x³-2x+8)

This example demonstrates:

  1. Rewriting subtraction as addition of the opposite
  2. Rearranging and grouping like terms
  3. Combining like terms
  4. Writing the final polynomial in descending order

Highlight: When subtracting polynomials, remember to add the opposite of the second polynomial. This effectively turns subtraction into addition.

The page includes several practice problems for adding and subtracting polynomials, providing students with opportunities to apply these techniques.

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

Free Study Notes from Top Students - Unlock Now!

Free notes for every subject, made by the best students

Get better grades with smart AI support

Study smarter, stress less - anytime, anywhere

Sign up with Email

By signing up you accept Terms of Service and Privacy Policy

Practice Problems: Adding and Subtracting Polynomials

This page contains a series of practice problems focused on adding polynomials and subtracting polynomials. The problems cover various scenarios, including:

  1. Adding polynomials with different degrees
  2. Adding polynomials with multiple variables
  3. Subtracting polynomials
  4. Combining addition and subtraction of polynomials

Each problem is presented with a step-by-step solution, reinforcing the techniques learned in the previous sections. The solutions demonstrate:

  • Proper alignment of like terms
  • Combining like terms
  • Writing polynomials in descending order

Example: (2a²-7a+10) + (a²+4a-7) = 3a²-3a+3

These practice problems provide valuable opportunities for students to apply their understanding of polynomial operations and gain confidence in their skills.

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

Free Study Notes from Top Students - Unlock Now!

Free notes for every subject, made by the best students

Get better grades with smart AI support

Study smarter, stress less - anytime, anywhere

Sign up with Email

By signing up you accept Terms of Service and Privacy Policy

Introduction to Polynomials

This page introduces key concepts related to polynomials and monomials.

A monomial is defined as a number, variable, or product of numbers and variables. Examples are provided to illustrate different types of monomials, such as 7 (a number), b (a variable), and 12xy² (a product of a number and variables).

The text then defines a polynomial as a variable expression made up of monomial terms. It explains that polynomials can be classified based on the number of terms:

  • A monomial is a polynomial with one term
  • A binomial has two terms
  • A trinomial contains three terms

Example: 7x² is a monomial, 4x+2 is a binomial, and 7x²+5x-7 is a trinomial.

The concept of descending order for polynomials is introduced, where terms are arranged so the exponents on the variable decrease from left to right.

Definition: The degree of a polynomial in one variable is the value of the largest exponent on the variable.

Example: The degree of 4x³-3x²+6x-1 is 3.

The page concludes with some additional notes on polynomial degree:

  • The degree of a nonzero constant is zero
  • Zero has no degree
HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

Free Study Notes from Top Students - Unlock Now!

Free notes for every subject, made by the best students

Get better grades with smart AI support

Study smarter, stress less - anytime, anywhere

Sign up with Email

By signing up you accept Terms of Service and Privacy Policy

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

Free Study Notes from Top Students - Unlock Now!

Free notes for every subject, made by the best students

Get better grades with smart AI support

Study smarter, stress less - anytime, anywhere

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Adding Polynomials

This page focuses on techniques for adding polynomials using both vertical and horizontal formats.

The key principle emphasized is combining like terms when adding polynomials. Two detailed examples are provided to illustrate the process:

Example 1 demonstrates adding polynomials using a vertical format: (2x²+x-1) + (3x³ + 4x²-5)

The solution shows how to:

  1. Arrange terms in descending order
  2. Align like terms in columns
  3. Combine terms in each column

Example 2 shows adding polynomials horizontally: (3x³-7x+2)+(7x²+2x-7)

This example illustrates:

  1. Using commutative and associative properties to rearrange terms
  2. Grouping like terms
  3. Combining like terms
  4. Writing the final polynomial in descending order

Highlight: When adding polynomials, the key is to identify and combine like terms, regardless of whether you use a vertical or horizontal format.

The page also introduces the concept of the opposite of a polynomial, where the sign of every term is changed. This is important for the subtraction of polynomials, which is introduced next.

HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

Free Study Notes from Top Students - Unlock Now!

Free notes for every subject, made by the best students

Get better grades with smart AI support

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Sign up with Email

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HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

Free Study Notes from Top Students - Unlock Now!

Free notes for every subject, made by the best students

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HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

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Free notes for every subject, made by the best students

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HW: 13-3339-57 (ad) rection 7.1 And Polynomials (1) Amaramial is a number, a vanable, or a product of numbers and variables. -FOR INSTANCE:

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Similar Content

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Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying