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## How To Add Simple Polynomials

**Adding polynomials**

To add two or more polynomials, again, combining the like terms skill helps a lot. If you are good at combining the like terms then adding polynomials is a piece of pie for you. When question asks you to add two or more polynomials, just collect the similar terms and add or subtract them according to the integer rules.

Consider we have a monomial “3x” and a trinomial “4x + 2y – 1” and we want to add them together. We have two options to add the given polynomials which are similar to simple arithmetic addition, hence, we can add them vertically or we can add them horizontally.

Let’s add both the polynomials by writing them vertically as shown below:

3x** **

__4x + 2y – 1__

**7x + 2y – 1 **

Care should be taken to write the similar terms in the same column as I wrote “3x” and “4x” in the same column. Note that there are no similar terms to “2y” and “- 1” in the first polynomial, which is a monomial having only one term. This is normal while adding polynomials. In such a case, just write the only terms in the bottom polynomial as the answer.

Let’s add the same polynomials by writing them horizontally as explained below:

(3x) + (4x + 2y – 1)

= 3x + 4x +2y – 1

= 7x + 2y – 1

So, write both the polynomials in brackets using plus (+) sign between them. Open the brackets without changing any signs. Collect the similar terms to get your answer.

I personally prefer to add polynomials writing them horizontally. Let’s do another example to better understand the concept:

**Example:** Simplify; **(7x – 3y – 9) + (- 5x + 6y – 9)**

As there is a plus sign between the brackets, open both the brackets without changing any sign as shown below:

**=****7x – 3y – 9 – 5x + 6y – 9**

Collect the similar terms and simplify them according to the integer rules in the next step;

**= 7x – 5x – 3y + 6y – 9 – 9 **

I used underline to show similar terms, you can use underlining too if you like. Now solve all the similar terms as; “7x – 5x = 2x”, “- 3y + 6y = +3y” and “- 9 – 9 = – 18”

Therefore our answer for the addition of the polynomials is given below:

= 2x + 3y – 18

That is the final answer.

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