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## How To Add Simple Polynomials

**Sum of polynomials**

To add two or more polynomials, again, combining like terms skill helps a lot. If you’re good at combining like terms, adding polynomials is a piece of cake for you. When the question asks you to add two or more polynomials, just collect the like terms and add or subtract them according to the rules for whole numbers.

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

Add the two polynomials by writing them vertically as shown below:

3x** **

__4x + 2y – 1__

**7x + 2y – 1 **

Be careful to write similar terms in the same column as I wrote “3x” and “4x” in the same column. Note that there are no terms like “2y” and “-1” in the first polynomial, which is a monomial that has only one term. This is normal when adding polynomials. In this case, just write the only terms of the lower polynomial as your answer.

We add the same polynomials by writing them horizontally as explained below:

(3x) + (4x + 2y – 1)

= 3x + 4x + 2y – 1

= 7x + 2y – 1

Therefore, write the two polynomials in parentheses using the plus sign (+) between them. Open the media without changing any signal. Collect the similar terms to get your answer.

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

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

Since there is one more sign between the brackets, open both brackets without changing any sign as shown below:

**=****7x – 3y – 9 – 5x + 6y – 9**

Collect the like terms and simplify according to the whole number rules in the next step;

**= 7x – 5x – 3 years + 6 years – 9 – 9 **

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

Therefore, our answer for the sum of the polynomials is given below:

= 2x + 3y – 18

This is the final answer.

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