# Writing Equivalent Expressions Worksheets

We will often come across algebraic expressions that hold the same value but are just written or composed slightly differently. At first, we learning this we will not see much value in identifying expressions that are equivalent to one another, but once you start applying this math in the real world it will become clear. You may be attempting to model a physical phenomenon of some kind with the use of expression and devise your own expression. You would then do some research to see if anyone else already modeled it, only to see that they used a different expression. But is it really different? Understanding equivalency can often help us make better decisions in this area. These worksheets and lessons will help students learn to rewrite expressions and make them equal to one another.

### Aligned Standard: HSA-SSE.A.2

- Equal Expressions Step-by-step Lesson- Find the expressions that match as far as equivalency.
- Guided Lesson - We work on simplifying, equivalence, and evaluating expressions.
- Guided Lesson Explanation - Some of these can be explained in two sentences; others require a bit of finesse.
- Practice Worksheet - Don't miss the line above the exponent area in this one on the first problem.
- Matching Worksheet - These are definitely the exact types of problems that you will see on tests for this skill.

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

### Homework Sheets

These questions are usually in multiple choice format. That is reflected in the homework pages.

- Homework 1 - We definitely cannot get these terms from our expression. That counts them out.
- Homework 2 - The exponent of a number tells you how many times it should be multiplied by itself.
- Homework 3 - Combine the like terms. Complete simplified.

### Practice Worksheets

With sheet one I threw in an exponent refresher because it appears a lot with this standard.

- Practice 1 - Evaluate each expression.
- Practice 2 - Simplify the expression.
- Practice 3 - Which expression is equal to the given expression?

### Math Skill Quizzes

We have you simplify, rewrite expressions and solve exponents. All big pot of math skills for you.

- Quiz 1 - See how low you can go with these.
- Quiz 2 - Complete the expression to make it equivalent to the given forms.
- Quiz 3 - Finish it off strong.

### How to Rewrite Expressions to Make Them Equivalent

Algebra has been haunting students since grade 4th. It strikes fear in the hearts of many because of the fact of being complicated. When we, as teachers, help explain the basic anatomy of these expressions to students, it becomes much easier for them. In retrospect, you are sometimes faced with expressions that are not fully spelled out, and in order to solve them, you need to write them in long form, which can be done with a few properties only.

Take a look at the following properties to rewrite the expressions to make them equivalent.

**Distributive Property** - Expressions are often written in form that uses a parenthesis to express the concept of a factor or multiple. This helps condense the expression, but can often misdirect you to not fully understand the significance of the expression.

Consider this example; 2x(3y + 2) - Start with 2x being multiplied with each and every element of the bracket. It will make it easier to walk through the process. Distributing 2x throughout the equation means multiplying 2x with 3y as well as with 2. The answer you will get after multiplying is 6xy + 4x. Now the expression you've got is the equivalent expression.

**Using Factoring** - Break down the equation in parts in order to find the equivalent expression. Separate the common factors. For example, it is the same expression; 6xy + 4x. In this expression, you need to identify the common factors an take them out, which in this case, is 2 for both elements.

2(3xy + 2x)

Now you can see another common factor, x. 2x(3y + 2). This gives you the equivalent expression, and you can write 6xy + 4x = 2x(3y + 2).