Addition of polynomials





Addition of polynomials is the topic in which we are going to see how to add two polynomials. Here you can find the clear examples with step by step explanation and also we have given worksheets based on the examples. Students can follow the examples and practice the worksheets and master in adding polynomials.

Definition of polynomials

An expression is the mathematical phrase that combines numbers and variables using the symbols like addition(+),subtraction (-), multiplication (x) and division (/). Expressions can be either simple or compound. If an expression consists of only one term is called simple expression.

Example:

2a,4xy,5ab

If an expression consists of two or more terms is called a compound expression.

Example:

4x + 3y, 5a + b + 3c and p + q + r + s

 The simple compound expressions without radical exponents are known as polynomials.

Addition of polynomials is nothing but adding like terms in the given polynomial. Before adding the polynomials let us know about the like terms.

Like terms are terms whose variables and their exponents(powers) must be same.

For example in the following polynomials 3x²y-7y+9 and 4x²y-5x+13

3x²y and 4x²y are like terms as both have x²y.

Addition of polynomials - Examples

Now let us see the addition of two polynomials.

           Polynomials can added either in vertical method  or horizontal method like in numerical addition. First let us add in the vertical method.

Example:

Add: 2x+3y-4 and 3x-3y+8

Solution:

                                 2x + 3y -4

                  +              3x  - 3y +8

                                 5x - 0y  +4

       Here we have added the polynomials with the like terms. It is simply like adding numbers.

Now let us see different example of adding two polynomials.

Example:

Add 3x²+2x-6 and 5x²-7x+8.

Solution:

     Here we will write the equations one below the other like in the previous example so that we can add the like terms easily.

                             3x² + 2x - 6

                 +          5x² - 7x  + 8

                             8x² - 5x  +2

Example:

    Now we will see an example in which we will add the polynomials horizontally.

Add: 4a²-7a+2 and 6a²+9a-25

Solution:

    First we will combine the like terms together.

                        = (4a²+6a²)+(-7a+9a)+(2-25)

                        =     10a²   +    2a     -23

                        =     10a²+2a-23

Students can follow the above examples and try to do the problems given in the worksheets on their own. Parents and teachers can guide them to do the problems on their own. They can verify the steps by referring to the solution. If you are having any doubt you can contact us through mail, we will help you to clear your doubts.