## Adding, Multiplying, and Subtracting Monomials

#### Aligned To Common Core Standard:

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

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

### Printable Worksheets And Lessons

- 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.

#### 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.