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How To Add Simple Polynomials

Adding polynomials

To add two or more polynomials, again combining the skills in similar terms helps a lot. If you are 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, simply collect the like terms and add or subtract them according to the integer rules.

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 is similar to simple arithmetic addition, therefore, we can add them vertically or we can add them horizontally.

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

3x

4x + 2a – 1

7x + 2y – 1

Care must be taken 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 with only one term. This is normal when adding polynomials. In such a case, simply write down only the terms of the lower polynomial as the answer.

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

(3x) + (4x + 2a – 1)

= 3x + 4x +2a – 1

= 7x + 2a – 1

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

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

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

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

=7x – 3y – 9 – 5x + 6y – 9

Group like terms together and simplify them according to integer rules in the next step;

= 7x – 5x – 3 years + 6 years – 9 – 9

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

Therefore, our answer for adding polynomials is given below:

= 2x + 3a – 18

This is the final answer.

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