# Addition of Polynomials – Definition, Rules, Examples | How do you Solve Polynomials with Addition?

The Addition of Polynomials is the process of adding different terms present in the polynomial. Check out the various problems and procedures on how do we add polynomials in this article. Know the different rules in addition of polynomials consisting of different exponents. Students of 6th Grade Math can get a strong grip on the Polynomial Addition by practicing the Addition of Polynomials Examples over here.

The addition of two polynomials is the process of combining like terms present in the two polynomials. Like terms are the terms those having the same variable and same exponent.

## How to Solve Addition of Polynomials? | Rules in Addition of Polynomials

We have given the process to add polynomials below. Follow the procedure given here to solve all the addition of polynomial problems.
(i) Arrange each polynomial along with their terms and also with the highest degree in decreasing order of degree.
(ii) Next, group the like terms whose variables and exponents are the same.
(iii) Finally, simplify by combining like terms.

Go through the below procedure to do the Horizontal addition of polynomials. Let’s check the Addition of Polynomials horizontally with a simple example.

Example: Find the sum of the following two polynomials:
12m4 + 3m3 + 8m – 5, 10m4 – 2m3 + 6m2 – 3m + 2.

Solution:
Given polynomials are 12m4 + 3m3 + 8m – 5 and 10m4 – 2m3 + 6m2 – 3m + 2.
The first polynomial is 12m4 + 3m3 + 8m – 5 and the second is 10m4 – 2m3 + 6m2 – 3m + 2.
Now, add the given polynomials horizontally.
(12m4 + 3m3 + 8m – 5) + (10m4 – 2m3 + 6m2 – 3m + 2)
Group the same variables with the same exponents. Terms that are not like terms cannot be added.
12m4 and 10m4 are the like terms.
3m3 and 2m3Â are the like terms.
8m and 3m are the like terms.
5 and 2 are constants.
Now, add the given polynomials with the like terms.
(12m4 + 3m3 + 8m – 5) + (10m4 – 2m3 + 6m2 – 3m + 2) = 12m4 + 3m3 + 8m – 5 + 10m4 – 2m3 + 6m2 – 3m + 2
12m4 + 10m4 + 3m3 – 2m3 + 6m2 + 8m – 3m – 5 + 2 = 22m4 + m3 + 6m2 + 5m – 3.

Therefore, the addition of given polynomials is 22m4 + m3 + 6m2 + 5m – 3.

The step-by-step process to Add Polynomials vertically is given here. Let’s check the Addition of Polynomials Vertically with a simple example.

Example:
Find the sum of the following two polynomials:
12m4 + 3m3 + 8m – 5, 10m4 – 2m3 + 6m2 – 3m + 2.

Solution:
Given polynomials are 12m4 + 3m3 + 8m – 5 and 10m4 – 2m3 + 6m2 – 3m + 2.
The first polynomial is 12m4 + 3m3 + 8m – 5 and the second is 10m4 – 2m3 + 6m2 – 3m + 2.
In the first term, we don’t have the m2 term. So, we can take it as 0.
Now, add the given polynomials vertically.
(12m4 + 3m3 + 0 + 8m – 5)
+ (10m4 – 2m3 + 6m2 – 3m + 2)
————————————
22m4 + m3 + 6m2 + 5m – 3

Therefore, the addition of given polynomials is 22m4 + m3 + 6m2 + 8m – 3.

Question 1.
Add: 6x + 4y, 5x â€“ 5y + 2z and -2x + 6y + 3z

Solution:
Given polynomials are 6x + 4y, 5x â€“ 5y + 2z and -2x + 6y + 3z.
The first polynomial is 6x + 4y and the second is 5x â€“ 5y + 2z and the third polynomial is -2x + 6y + 3z.
Now, add the given polynomials horizontally.
(6x + 4y) + (5x â€“ 5y + 2z) + (-2x + 6y + 3z)
Group the same variables with the same exponents. Terms that are not like terms cannot be added.
6x, 5x, and 2x are the like terms.
4y, 5y, and 6y are the like terms.
2z and 3z are the like terms.
Now, add the given polynomials with the like terms.
(6x + 4y) + (5x â€“ 5y + 2z) + (-2x + 6y + 3z) = 6x + 4y + 5x â€“ 5y + 2z -2x + 6y + 3z
6x + 5x -2x+ 4y â€“ 5y + 6y + 2z + 3z = 9x + 5y + 8z.

Therefore, the addition of given polynomials is 9x + 5y + 8z.

Question 2.
Add: 6a2 + 2ab â€“ 2b2, -2a2 + 4ab + 6b2 and 6a2 â€“ 20ab + 8b2

Solution:
Given polynomials are 6a2 + 2ab â€“ 2b2, -2a2 + 4ab + 6b2 and 6a2 â€“ 20ab + 8b2.
The first polynomial is 6a2 + 2ab â€“ 2b2, and the second is -2a2 + 4ab + 6b2 and the third polynomial is 6a2 â€“ 20ab + 8b2.
Now, add the given polynomials horizontally.
(6a2 + 2ab â€“ 2b2) + (-2a2 + 4ab + 6b2) + (6a2 â€“ 20ab + 8b2)
Group the same variables with the same exponents. Terms that are not like terms cannot be added.
6a2, -2a2, and 6a2 are the like terms.
2ab, 4ab, and 20ab are the like terms.
2b2, 6b2, and 8b2Â are the like terms.
Now, add the given polynomials with the like terms.
(6a2 + 2ab â€“ 2b2) + (-2a2 + 4ab + 6b2) + (6a2 â€“ 20ab + 8b2) = 6a2 + 2ab â€“ 2b2 -2a2 + 4ab + 6b2 + 6a2 â€“ 20ab + 8b2
6a2 – 2a2 + 6a2 + 2ab + 4ab â€“ 20ab â€“ 2b2 + 6b2 + 8b2 = 10a2 – 18ab â€“ 12b2

Therefore, the addition of given polynomials is 10a2 – 18ab â€“ 12b2.

Question 3.
Add: 9a + 7b, 8a â€“ 8b + 5c and -7a + 9b + 6c

Solution:
Given polynomials are 9a + 7b, 8a â€“ 8b + 5c and -7a + 9b + 6c.
The first polynomial is 9a + 7b and the second is 8a â€“ 8b + 5c and the third polynomial is -7a + 9b + 6c.
In the first term, we don’t have the c term. So, we can take it as 0.
Now, add the given polynomials vertically.
9a + 7b + 0
8a – 8b + 5c
-7a + 9b + 6c
——————
10a +8b + 11c

Therefore, the addition of given polynomials is 10a +8b + 11c.

Question 4.
Add: 5x3 â€“ 7x2 + 10x + 20, 17x3 â€“ 4x â€“ 25, 11x2 â€“ 2x + 17 and -10x3 + 4x2 â€“ 9x.

Solution:
Given polynomials are 5x3 â€“ 7x2 + 10x + 20, 17x3 â€“ 4x â€“ 25, 11x2 â€“ 2x + 17 and -10x3 + 4x2 â€“ 9x.
The first polynomial is 5x3 â€“ 7x2 + 10x + 20 and the second is 17x3 â€“ 4x â€“ 25, and the third polynomial is 11x2 â€“ 2x + 17 also the fourth polynomial is -10x3 + 4x2 â€“ 9x.
Where the variable is not present we can take it as 0.
Now, add the given polynomials vertically.
5x3 â€“ 7x2 + 10x + 20
17x3 + 0Â  Â â€“ 4x â€“ 25
0Â  Â  + 11x2 â€“ 2x + 17
-10x3 + 4x2 â€“ 9x + 0
———————–
12x3 + 8x2 – 5x + 12

Therefore, the addition of given polynomials is 12x3 + 8x2 – 5x + 12.

### FAQs on Addition of Polynomials

1. Â What is a linear Polynomial?

The linear polynomial is a polynomial that has the degree 1.

Â 2. How do we add polynomials?

We find similar terms first then we add the coefficients of the terms to add those polynomials.

Â 3. Is it possible to add different terms with different exponents?

No, generally we add similar terms having the same exponents.

4. Add 3x + 2y and 4x + 3y?

By adding the given polynomials, we can get 7x + 5y.

5. Add 2a + 9b and 3a?

By adding the given polynomials, we can get 5a.

### Conclusion

The complete article will help you to learn the addition of polynomials easily. Without missing any part, read the complete concept and gain the knowledge.

Scroll to Top
Scroll to Top