# Polynomial Addition and Subtraction Worksheets

Processing these operations is all about staying organized and spotting like terms found within each set of polynomials. If we remember back, like terms consist of the same variable and powers of exponents that are the same. Coefficients (the multipliers in front) can be different because they just indicate a multiple of the term. Addition is just the act of putting like terms together and pay attention to operators that exist. I find it helpful to have students draw curves to indicate which terms they are grouping together. That way, if there is a calculation error, it is easy to spot. When we are subtracting, we are just taking like terms away from one another. It is helpful to just flip (reverse) the sign of each term in the subtrahend portion. These worksheets will test your ability to stay focused and organized.

### Aligned Standard: HSA-APR.A.1

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

- Quiz 1 - (3z
^{2}+ 5z + 3) + (4z + 4) - Quiz 2 - Use algebra tiles to add (3y + 3) + (2y + 2)
- Quiz 3 - Place all of these things together to get a final review in.

### 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 and a constant; 3 x 2, 4y, and z.

Similar to monomials, the addition and subtraction of polynomial also follow the rules 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 x 2 + 5y + 2z as the second expression and add them.

(3 x 2 + 4y + z) + (2 x 2 + 5y + 2z)

(6 + 4y + z) + (4 + 5y + 2z) : Process multiplication operators.

6 + 4y + z + 4 + 5y + 2z : Remove the parentheses and write like terms together.

(6 + 4) + (4y + 5y) (x + 2z): We add like terms.

10 + 9y +3z

Note how the coefficients have added up while the variable and exponents (if present) 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)

3x + 4y + 2z - 2x - 3y - z : Remove the parentheses and change the signs of subtrahend polynomial.

3x - 2x + 4y - 3y + 2z – z: Write the like terms together with their changed signs.

Remember to write the sign of greater coefficient with your answer: x + y + z.