Subtracting Polynomials

Subtracting polynomials is a method of subtracting polynomials by converting the signs to the opposite sign. The method is similar to adding polynomials. While subtracting polynomials, we convert the sign to either positive or negative depending on the actual equation. Let us learn more about subtracting polynomials, the methods, the steps, and solve a few examples.

Subtracting polynomials is very similar to adding polynomials where the minus sign is converted through the parentheses. There are two methods of subtracting polynomials - vertically and horizontally. The like terms in the polynomials are separated to make the subtraction simple. Using columns would help us to match the correct terms together in a complicated subtraction. Keep two rules in mind while performing the subtraction of polynomials:

• Rule 1: Always take like terms together while performing subtraction.
• Rule 2: Signs of all the terms of the subtracting polynomial will change, + changes to - and - changes to +.

Subtracting polynomials is done in two methods - vertically and horizontally. In both methods, the rules mentioned above are applicable. In the horizontal method, the signs through the parentheses of the second equation change to perform simple addition. In the vertical method, the equations are written column-wise according to the terms, the signs are converted and subtraction takes place. Let us see the steps to perform subtraction of polynomials in both methods.

Method 1: Subtracting Polynomials Horizontally

• Step 1: Arrange the polynomials in their standard form.
• Step 2: Place the polynomial next to each other horizontally.
• Step 3: Change the signs of the second polynomial through the parentheses to its opposite sign.
• Step 4: Separate the like terms and arrange them together.
• Step 5: Perform the calculations.

Let us look at an example to understand this better.

For example: Subtract 4x - 10y + 15z from 5x + 8y - 20z

Step 1: Arrange the polynomials in standard form. In this example, it is already arranged.

Step 2: Place them horizontally.

(4x - 10y + 15z) - (5x + 8y - 20z)

Step 3: Change the sign of the second polynomial through the parentheses.

4x - 10y + 15z - 5x - 8y + 20z

Step 4: Arrange the like terms together.

4x - 5x - 10y - 8y + 15z + 20z

Step 5: Solve the equation

-x - 18y + 35z

Therefore, when we subtract 4x - 10y + 15z from 5x + 8y - 20z = -x - 18y + 35z.

Method 2: Subtracting Polynomials Vertically

Subtracting polynomials vertically is done in a very simple manner. Once the polynomials have been arranged vertically, the signs in the second polynomials are converted from plus to minus and minus to plus without the requirement of the parentheses. This is also a shortcut method for subtracting two or more polynomials. Polynomials can be subtracted in vertical arrangement using the steps given below,

• Step 1: Arrange the polynomials in their 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: We can represent the missing power term in the standard form with "0" as the coefficient to avoid confusion while arranging terms.
• Step 4: The signs of the terms in the second polynomials change as done in a horizontal manner.
• Step 5: Perform the calculations

Let us look at an example.

For example: Subtract 4x² + 8x + 10 from 5x²- 14x - 15

• Step 1: Arranging the polynomial in standard form. In this case, they are already in their standard forms.
• Step 2: Like terms in the above two polynomials are: 4x² and 5x², 8x and -14x, 10 and -15.
• Step 3: Enclose the part of the polynomial which to be deducted in parentheses with a negative (-) sign prefixed. Then, remove the parentheses by changing the sign of each term of the polynomial expression.
• Step 4: Calculate after altering the signs of the subtracting polynomials:

Related Topics

Listed below are a few topics that are related to subtracting polynomials, take a look

• Standard Form of Polynomials
• Polynomial Expressions
• Adding and Subtracting Polynomials

What is Meant by Subtracting Polynomials?

Subtracting polynomials is very similar to adding polynomials but while subtracting we change the signs from plus to minus and minus to plus. Subtracting polynomials is done in two methods - vertically and horizontally. In both methods, when a minus sign is mentioned before the parentheses, we always change the signs.

What is the Rule in Subtracting Polynomials?

While subtracting polynomials, the two important rules are:

• Rule 1: Always take like terms together while performing subtraction.
• Rule 2: Signs of all the terms of the subtracting polynomial will change, + changes to - and - changes to +.

What Property is Used When Subtracting Polynomials?

While subtracting polynomials, we can use the distributive property. This is even applicable while adding polynomials. For example (3x² + 2x + 6) + (x² - 6x - 10) = (3 + 1)x² + (2 - 6)x + (6 - 10) = 4x² - 4x - 4.

What are the Steps of Subtracting Polynomials Horizontally?

The important step before subtracting a polynomial is converting the subtraction problem to an addition problem by converting minus to plus and plus to minus. The steps to subtract polynomials horizontally are:

• Arrange the polynomials in their standard form.
• Place the polynomial next to each other horizontally.
• Change the signs of the second polynomial through the parentheses to its opposite sign.
• Separate the like terms and arrange them together.
• Perform the calculations.

What are the Steps of Subtracting Polynomials Vertically?

Subtracting polynomials vertically is also done by converting the problem from subtraction to addition. Arrange the polynomials vertically or column-wise one below the other according to the like terms and calculate. Here are the steps:

• Arrange the polynomials in their standard form
• Place the polynomials in a vertical arrangement, with the like terms placed one above the other in both the polynomials.
• We can represent the missing power term in the standard form with 0 as the coefficient to avoid confusion while arranging terms.
• The signs of the terms in the second polynomials change as done in a horizontal manner.
• Perform the calculations.

How Do You Simplify Subtracting Polynomials?

To simplify subtracting polynomials, the first step is to convert the problem from subtraction to addition. The signs in the second polynomial while placed horizontally are converted through the parentheses i.e. minus to plus and plus to minus. Once the polynomials are converted, normal addition of polynomials is performed.