Addition and Subtraction of Polynomials

Addition of polynomials means we simply add the like terms. 

so, what is “Like terms”?

Like terms are terms that have the variables, and powers are same, and coefficients of terms can be different. 

Example:  

1.          Yes          2x,  -5x,  11x,  

                 Yes, all are like terms,

because, the variables of all term are same that is x.

2.          Yes      7x²y^{2 ,}   -3x²y^{2 ,}   x²y²  

             Yes, all are like terms,because, the

 variables of all term are same that is  x²y².

3.           No     x²y,   4x²y²

 No, all are not like terms, because the variables and their powers are different.

Addition of Polynomials 

There are two methods for Addition of Polynomials

1. Horizontal method

2. Vertical method

Horizontal method

Example 1: Add (4x + 9y) + (3x – 5y)

                    First we solve parentheses,

                         4x + 9y + 3x – 5y

Now we write the problem in addition form, thus the required addition is 

                       4x + 9y + 3x – 5y

Now we rewrite all like terms together or Combine like terms and then add all like terms. 

4x + 3x+ 9y – 5y

                                7x + 4y

These terms are unlike terms because they have different variables so cannot combine,

Therefore, solution is  7x + 4y

Example 2:  Add  7x² + 3x + 5  and  2x² + 4x – 3

First we write the problem in addition form, thus the required addition is 

              7x² + 3x + 5  +  2x² + 4x – 3

Now we rewrite all like terms together or Combine like terms and then add all like terms. 

             (7x² + 2x²  ) +   (3x + 4x)   + (5 – 3)

Combine like terms 

9x² + 7x + 2  This is the solution. 

Example 3: Add   5x⁴+ 3x² + 5  and  2x² + 6x – 4

First we write the problem in addition form, thus the required addition is 

              5x⁴ + 3x² + 5  +  2x² + 6x – 4

Now we rewrite all like terms together or Combine like terms and then add all like terms. 

               5x⁴ + ( 3x² + 2x² ) + 6x + (5 – 4)

Combine like terms 

                        5x⁴ + 5x² + 6x + 1  

This is the solution. 

 Vertical method

Example 1: Add (4x + 9y) + (3x – 5y)

                    First we solve parentheses,

                         4x + 9y + 3x – 5y

Now we rewrite all like terms with their signs, to one below the other in same vertical columns and then add all like terms of different groups.
                              4x + 9y 
                              3x – 5y  

                              7x + 4y

Therefore, solution is  7x + 4y

Example 2: Add   4x² + 2x + 7  and  3x² + 5x – 6

Original problem is,

              4x² + 2x + 7  +  3x² + 5x – 6

Now we rewrite all like terms with their signs, to one below the other in same vertical columns and then add all like terms of different groups

4x² + 2x + 7                           

3x² + 5x – 6 

________________

 7x² + 7x + 1  solution.

Example 3: Add  4x³ + 3x² + 7  and  3x³ + 8x² – 2

Original problem is,

        4x³ + 3x² + 7  +  3x³ + 8x² – 2      

Now we rewrite all like terms with their signs, to one below the other in same vertical columns and then add all like terms of different groups.

4x³ + 3x² + 7                         

 3x³ + 8x² – 2

_________________                       Add like terms,  7x³ + 11x² + 5  solution.