 # Subtraction of Polynomials – Definition, Methods, Rules, Examples | How to do Subtraction of Polynomials?

Subtraction of Polynomials is done by converting the signs to the opposite sign of subtracting polynomials. The concept of Subtraction of Polynomials is also the same as the Addition of Polynomials but the tricky part is with the signs involved in subtraction.

The positive sign is converted to the negative sign and the negative sign is converted to the positive sign of the subtracting polynomial before subtraction. Students of the 6th Grade Math can get a complete grip on the concept by answering the Subtracting Polynomials Questions explained step by step. In addition, you can find information on What is Polynomial Subtraction, How to Subtract Polynomials, etc.

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## Subtraction of Polynomials Definition

The process of subtracting polynomials is very similar to the Addition of Polynomials. Firstly, take two polynomials and find out the subtracting polynomial. You can go through two processes to subtract polynomials. They are Subtraction Polynomials Horizontally and Subtraction Polynomials Vertically.

## How do we Subtract Polynomials?

You must follow two different rules to subtract polynomials. They are explained clearly below

• Rule 1: Group the like terms together to perform subtraction.
• Rule 2: Signs of all the terms of the subtracting polynomial must change, positive to negative and negative changes to positive.

### Subtracting Polynomials Horizontally

In the horizontal method, the signs present in the parentheses of the second equation will change to perform simple addition. The steps to subtract Polynomials Horizontally are

(i) Firstly, Arrange the given polynomials in their standard form.
(ii) Then, place the polynomials next to each other horizontally by finding the subtracting polynomial.
(iii) Place the second polynomial in the parenthesis and convert all the terms signs, then remove the parenthesis.
(iv) Group the like terms and arrange them together.
(vi) Then, finally find out the answer by doing proper calculations.

Example:
Subtract 3a – 9b + 14c from 4a + 7b – 19c

Soluion: Given polynomials are 3a – 9b + 14c and 4a + 7b – 19c.
The first polynomial is 4a + 7b – 19c and the second is 3a – 9b + 14c.
Place these polynomials horizontally and keep the parenthesis.
(4a + 7b – 19c) – (3a – 9b + 14c)
Change the sign of the second polynomial presented in the parenthesis. Then, remove the parenthesis
(4a + 7b – 19c) – (3a – 9b + 14c) = 4a + 7b – 19c – 3a + 9b – 14c.
Arrange the like terms together.
4a and 3a are like terms.
7b and 9b are like terms.
19c and 14c are like terms.
4a – 3a + 7b + 9b – 19c  – 14c = a + 16b – 10c

Therefore, the addition of given polynomials is a + 16b – 10c.

### Subtracting Polynomials Vertically

In the vertical subtraction of the polynomial, the equations are written column-wise according to the terms, and also the signs are converted and subtraction takes place.

At first, arrange the polynomials in their standard form
(ii) Find out the subtracting term and place the polynomials in a vertical arrangement.
Place them with the like terms placed one above the other in both the polynomials.
(iii) If you find any missing term in the polynomial, then consider it as 0.
(iv) The signs of the second polynomial can change in a horizontal manner.

Example:
Subtract 5m2 + 9m + 11 from 6m2– 15m – 16

Solution:
Given polynomials are 5m2 + 9m + 11 and 6m2– 15m – 16.
The first polynomial is 6m2– 15m – 16 and the second is 5m2 + 9m + 11.
Now, do the subtraction of given polynomials vertically.
6m2– 15m – 16
5m2 + 9m + 11
–      –      –
——————–
m2 – 24m – 27

Therefore, the subtraction of given polynomials is m2 – 24m – 27.

### Subtraction of Polynomials Examples with Answers

Below are the different examples on Subtraction of Polynomials. Practice every problem and understand the concept easily.

Question 1.
Subtract: 3p – 21q + 5r from 9p + 26q – 7r.

Soluion:
Given polynomials are 3p – 21q + 5r and 9p + 26q – 7r.
The first polynomial is 9p + 26q – 7r and the second is 3p – 21q + 5r.
Place these polynomials horizontally and keep the parenthesis.
(9p + 26q – 7r) – (3p – 21q + 5r)
Change the sign of the second polynomial presented in the parenthesis. Then, remove the parenthesis
(9p + 26q – 7r) – (3p – 21q + 5r) = 9p + 26q – 7r – 3p + 21q – 5r.
Arrange the like terms together.
9p and 3p are like terms.
26q and 21q are like terms.
7r and 5r are like terms.
9p – 3p + 26q + 21q – 7r  – 5r = 6p + 47q – 12r

Therefore, the addition of given polynomials is 6p + 47q – 12r.

Question 2.
Subtract:  -7y2 – 9x3 + 16z from 2y2 – x3 + z.

Soluion:
Given polynomials are -7y2 – 9x3 + 16z and 2y2 – x3 + z.
The first polynomial is 2y2 – x3 + z and the second is -7y2 – 9x3 + 16z.
Place these polynomials horizontally and keep the parenthesis.
(2y2 – x3 + z) – (-7y2 – 9x3 + 16z)
Change the sign of the second polynomial presented in the parenthesis. Then, remove the parenthesis
(2y2 – x3 + z) – (-7y2 – 9x3 + 16z) = 2y2 – x3 + z + 7y2 + 9x3 – 16z
Arrange the like terms together.
2y2 and 7y2 are like terms.
x3 and 9x3 are like terms.
z and 16z are like terms.
2y2 + 7y2 – x3 + 9x3 + z – 16z = 9y2 + 8x3 – 15z

Therefore, the addition of given polynomials is 9y2 + 8x3 – 15z.

Question 3.
Subtract: a – 4b – 2c from 7a – 3b + 6c.

Soluion:
Given polynomials are a – 4b – 2c and 7a – 3b + 6c.
The first polynomial is 7a – 3b + 6c and the second is a – 4b – 2c.
Find the like terms from the above polynomials.
7a and a are like terms.
– 3b and – 4b are like terms.
6c and – 2c are like terms.
Now, do the subtraction of given polynomials vertically.
7a – 3b + 6c
a – 4b – 2c
–    +    +
——————–
6a + b + 8c

Therefore, the subtraction of given polynomials is 6a + b + 8c.

Question 4.
Subtract: 4a3 + 6a2 – 8a + 11 from 7a3 – 9a2 + 2a + 11.

Soluion:
Given polynomials are 4a3 + 6a2 – 8a + 11 and 7a3 – 9a2 + 2a + 11.
The first polynomial is 7a3 – 9a2 + 2a + 11 and the second is 4a3 + 6a2 – 8a + 11.
Find the like terms from the above polynomials.
7a3 and 4a3 are like terms.
– 9a2 and 6a2 are like terms.
2a and – 8a are like terms.
11 and 11 are like terms.
Now, do the subtraction of given polynomials vertically.
7a3 – 9a2 + 2a + 11
4a3 + 6a2 – 8a + 11
–     –        +      –
——————–
3a3 – 15a2 + 10a + 0

Therefore, the subtraction of given polynomials is 3a3 – 15a2 + 10a.

### FAQs on Subtracting Polynomials

1. What is Meant by Subtracting Polynomials?

Subtracting polynomials is the process of subtraction where the second term of the polynomial signs is changed.

2. What are the types of Subtracting polynomials?

We can follow the horizontal subtraction of polynomials and vertical subtraction of polynomials.

3. What is the Rule in Subtracting Polynomials?

We must follow the below rules for the subtraction of polynomials. They are

• Rule 1: Take like terms together while doing subtraction.
• Rule 2: Must change the signs of all the terms of the subtracting polynomial, positive to negative and negative to positive.

4. What is the simple way of Subtracting Polynomials?

First, convert the problem from subtraction to addition by replacing the subtracting polynomial. By converting the problem from subtraction to addition, you can easily simplify it.

5. Subtract 3x – 2 from 4x + 4

The subtraction of given polynomials 3x – 2 and 4x + 4 is x + 2.

### Summary

Read the entire article and solve every problem given in this article. We have given easy procedure to solve the problems. Also, the entire article is explained in a simple way to make you learn everything about the subtraction of the polynomial.

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