## Polynomial Addition and Subtraction

#### Aligned To Common Core Standard:

**High School** - HSA-APR.A.1

How to Add and Subtract Polynomials?
By now, you have an understanding of exponents and variables. In fact, you must be familiar with monomials as the singular terms having variables and coefficients
If we write these monomials together with a plus or minus sign, we get a polynomial. It is that simple. The sum or difference of monomials is termed as a polynomial.
A polynomial usually looks like this: 3 x 2 + 4y + z
The above expression is the sum of three monomials; 3 x 2, 4y, and z
Similar to monomials, the addition and subtraction of polynomial also follow the rule of like terms. That is, the coefficients with the same variables are added or subtracted but the variables and exponents stay the same.
**Adding polynomials** - Let's explore how the like terms work with polynomials.
Let's take one expression to be 3 x 2+ 4y + z and 2 x2 + 5y + 2z as the second expression, and add them.
(3 x 2 + 4y + z) + (2 x 2 + 5y + 2z)
Remove the parentheses and write like terms together
3 x 2 + 2x2 + 4y + 5y + z + 2z
5 x 2 + 9y + 3z
Note how the coefficients have added up while the variable and exponents remain the same
**Subtracting polynomials** - Similar to addition, subtraction also follows the rule of like terms. However, you need to pay close attention to the change of signs
Let's take 3x + 4y + 2z and 2x + 3y + z, as two expressions: (3x + 4y + 2z) – (2x + 3y + z)
Remove the parentheses and change the signs of subtrahend polynomial: 3x + 4y + 2z – 2x - 3y - z
Write the like terms together with their changed signs: 3x - 2x + 4y - 3y + 2z - z Remember to write the sign of greater coefficient with your answer: x + y + z

### Printable Worksheets And Lessons

- Algebra Tiles Step-by-step
Lesson- Combine like terms in a polynomial while seeing it visually.

- Guided Lesson
- We get into more operation work with polynomials.

- Guided Lesson Explanation
- Work with the like terms first and then delve into the use of
operations.

- Practice Worksheet
- Start with a few visuals and then move into basic sums and differences
of polynomials.

- Matching Worksheet
- Match the polynomial operations to their final output, in some
cases simplified output.

- Addition and Subtraction
of Polynomials Five Packet - Work on mass practice for your
sums and differences.

#### Homework Sheets

The second sheet is done visually. Students will pick up on it quickly.

- Homework 1 - We cannot combine 5a^2 and 9a because they are not like terms.
- Homework 2 - These algebra boxes represent the addition problem. We have use the algebra tiles to solve the addition problems.
- Homework 3 - Like terms are terms that have the same variables raised to the same powers.

#### Practice Worksheets

The blocks are the middle sheet as well here.

- Practice 1 - We have to add like terms and their coefficients.
- Practice 2 - Use algebra tiles to add (1k + 6) + (3k + 2).
- Practice 3 - Find the final value of the following problems.

#### Math Skill Quizzes

I like to have the kids get of the habit of thinking of each polynomial as three separate parts.