# Adding, Multiplying, and Subtracting Monomials Worksheets

How to Add, Multiply, and Subtract Monomials?
You must have come across several algebraic expressions. Some have one variable; some have more than two and some variables are even raised to the powers.
Well, there are different types of these algebraic expressions. But for now, we are going to investigate one such expression.
**Monomial expression** - Let's start with the simplest expression, a monomial.
An algebraic expression that consists of one term is called monomial. You can easily remember this by learning that 'mono' in monomial means one. So, a monomial is a one-term algebraic expression.
Moving on to learning the basic mathematical operations with monomial.
**Adding monomials** - Two or more monomials can be added only when they are like terms.
Like terms are those expressions that have identical variables and exponents. They may or may not have different coefficients.
While adding monomials, you only add the coefficients and the variables stay the same .
For example; 2 x 2y + 3 x 2y = 5 x 2y. Notice only the coefficients have added up, while the variables and exponents remained unchanged.
**Subtracting monomials** - The subtraction of monomial follows the same rules as with addition. The coefficients are subtracted from, each other while the variables are not changed
For example; 3 x 2y – 2 x 2y = 1 x 2y. The coefficients are subtracted, but the variables stay the same. **Multiplying monomials** - Multiplication of monomial is different from addition and subtraction. In multiplication, both coefficient and variables are multiplied.
With variable multiplication, we use the rule of power. That is, the exponents of bases are added. For example; (5x)(5 x 2) = 5.5 (x 1 + 2) = 25 x 3

### Aligned Standard: **Related to HSA-APR.A.1**

- Adding, Subtracting Monomials Lesson- It is a sunny day for monomials. You can use this section as a warm-up for polynomials.
- Multiplying Monomials Lesson - Remember that when you multiply exponents, you basically add the values.
- Adding & Subtracting Monomials Worksheet 1 - We start off simple and throw two or three slightly difficult problems in there.
- Multiplying Monomials Worksheet 3 - The difficulty level is slightly higher here than the sheets below.
- Adding & Subtracting Monomials Homework - Why not send them home with a brief reminder of what you worked on today.

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

### Homework Sheets

These are great for extra work that make all the difference in your week.

- Homework 2 - Adding & Subtracting: Find each sum or difference.
- Homework 3 - Multiplication: Find each product.
- Homework 4 - More Multiplying: Determine the end values after multiplying monomials.

### Practice Worksheets

These should print out fully spaced and with answer keys.

- Add & Subtract Worksheet 2 - Find each sum or difference.
- Multiplying Practice 4 - The first problem has the variable "i" as in "Irene".

### Math Skill Quizzes

A quiz on each of the skills. Of course sums and differences are together.

- Adding & Subtracting Quiz 1 - A helpful quiz sheet.
- Multiplying Quiz 2 - Don't get thrown when a variable has no number in front of it, it is equal to one.

### When Do We Apply These Operations?

It should be noted that we can only add or subtract monomials if they contain like terms. This means that they contain the same variables and corresponding exponents. The coefficients on these like terms may be different and that is where our operators indicate what to do with them. When we are performing multiplication operations it is important to note that we should be focused on the coefficients first and then we process the variables by finding the sum of the exponents. This will help in many different situations where are attempting to simplify expressions to give us something that easier to work with.