Polynomials are algebraic expressions that consist of constants and variables of different powers. Adding polynomials is a way of combining and summing up terms having the same power. We will be learning about different methods of adding polynomials in this article.
|1.||Adding Polynomials Definition|
|2.||Steps in Adding Polynomials|
|3.||FAQs on Adding Polynomials|
Adding Polynomials Definition
Adding polynomials is defined as the addition operation of polynomials. Polynomials are algebraic expressions of different degrees. While adding polynomials we follow some specific rules which makes it very simple to do the operation.
Rules of Adding Polynomials
Look at the two important rules of adding polynomials given below:
- Rule 1: The like terms are always combined and added. Unlike terms can never be added.
- Rule 2: While adding the terms, the sign always remains the same.
Before learning the method of adding polynomials, let us first quickly go through the meanings of like terms and unlike terms in any polynomial.
Like terms are defined as algebraic terms which have the same variables along with the same exponents. For example, 2x, 7x, -2x, etc are all like terms.
Unlike terms are the algebraic terms which do not have the same variables along with the same exponents. For example, 2, 7x2, -2y2, etc are all unlike terms.
Adding Polynomials Steps
We can add polynomials using different methods. Let us briefly discuss two different methods to add polynomials along with their steps and examples shown below.
Adding Polynomials Horizontally
For adding polynomials horizontally, we place the given polynomials in a horizontal manner. Let's understand the steps below to add polynomials horizontally.
- Step 1: Write the polynomials in a horizontal manner with an addition (+) sign between them.
- Step 2: Combine the like terms together by clubbing them in parentheses by retaining the sign of every term.
- Step 3: Perform the calculations.
Here's an example to show the horizontal addition of polynomials.
Example: Add the polynomials 5x2 + 3x - 2 and 3x2 - x + 4 horizontally.
Following the steps above,
Step 1: 5x2 + 3x - 2 + 3x2 - x + 4
Step 2: (5x2 + 3x2) + (3x - x) + (- 2 + 4)
Step 3: 8x2 + 2x + 2
Thus, the addition of polynomials 5x2 + 3x - 2 and 3x2 - x + 4 is equal to 8x2 + 2x + 2.
Adding Polynomials Vertically
For adding polynomials vertically, we place the polynomials column-wise vertically. Hence, it is known as the vertical method of adding polynomials. Let's understand the steps below to add polynomials vertically.
- Step 1: Write the polynomials in standard form.
- Step 2: Place the polynomials in a vertical arrangement, with the like terms placed one above the other in both the polynomials.
- Step 3: If any power term is missing in any polynomial, we write a '0' as its coefficient to avoid confusion in the column-wise arrangement.
- Step 4: Perform the calculations by retaining the sign of the terms.
Here's an example to show the vertical addition of polynomials.
Example: Add the polynomials 2x2 + 3x + 2 and 3x2 - 5x -1 vertically.
The polynomials 2x2 + 3x + 2 and 3x2 - 5x -1 are written in standard form. Let's arrange them vertically and perform the calculations as shown below.
Therefore, on adding 2x2 + 3x +2 and 3x2 - 5x -1 we get 5x2 - 2x + 1.
Check the following articles related to the concept of adding polynomials.
Adding Polynomials Examples
Example 1: Use the concept of adding polynomials to add 9x2 - 3x and - 6x2 + 8x - 3.
Solution: The given polynomials are 9x2 - 3x and - 6x2 + 8x - 3. We have to perform (9x2 - 3x) + (- 6x2 + 8x - 3). Clubbing the like terms we get,
(9x2 + (- 6x2)) + (- 3x + 8x) + (- 3)
= (9x2 - 6x2) + (- 3x + 8x) + (- 3)
= 3x2 + 5x - 3
Thus, on adding 9x2 - 3x and - 6x2 + 8x - 3 we get the result as 3x2 + 5x - 3.
Example 2: Using the concept of adding polynomials, add the expressions 5x3 - 2x2 + x - 3 and - 2x3 + x2 + 5x + 1 vertically.
Solution: Let's arrange the given polynomials 5x3 - 2x2 + x - 3 and - 2x3 + x2 + 5x + 1 vertically by placing the like terms one below the other followed by performing the calculation as shown below.
Thus, on adding the polynomials 5x3 - 2x2 + x - 3 and - 2x3 + x2 + 5x + 1 vertically, we get the result as 3x3 - x2 + 6x - 2.
FAQs on Adding Polynomials
What is Adding Polynomials?
Adding polynomials is defined as summing up the like terms of two or more algebraic expressions by retaining their sign to get the result. It is very similar to a regular addition operation. For example: Let's add 3x + 8 and - 2x + 1. This will be (3x - 2x) + (8 + 1) = x + 9.
What Terms can be Combined in Adding Polynomials?
While adding polynomials, only like terms can be combined together i.e., terms with the same power on the variable can be combined such as 7x2, 9x2 or 6x, 4x, and so on.
What are the Steps in Adding Polynomials?
While adding polynomials, the given polynomials are written in standard form by arranging them from the highest power to the lowest power variable followed by combining the like terms without changing their sign and performing the calculation. If any term does not have a like term then it remains the same. For example, let's add - 4y2 + 5 and 2y2 + 5y - 2. This implies, (- 4y2 + 2y2) + 5y + (5 - 2) = - 2y2 + 5y + 3.
What is the First thing to Consider in Adding Polynomials?
The first thing to be considered in adding polynomials is to arrange the given polynomials in standard form followed by combining the like terms.
How to Solve Adding Polynomials?
We can do the addition of polynomials by combining the like terms of the given polynomials and adding them further. For example, 7m - 2 and 8 + 6m can be added as (7m + 6m) + (- 2 + 8) = 13m + 6.
How is Adding Integers similar to Adding Polynomials?
Adding integers is similar to adding polynomials as they have both positive and negative parts. For example: The sum of two polynomials - 3y and 2y = - 3y + 2y = - y and the sum of two integers 1 and - 6 = 1 + (- 6) = 1 - 6 = - 5.
How to find the Perimeter by Adding Polynomials?
The perimeter of a polygon is defined as the sum of all the sides of the given polygon. Let's assume a square has a side length of 5x, hence the perimeter can be calculated as the sum of all four sides i.e., 5x + 5x + 5x + 5x = 20x. Thus, we see that whenever the sides of a given polygon are given in the form of a polynomial, the perimeter is calculated by the addition of polynomials.