# Equivalent Expressions – Part 1

## Overview

Equivalent expressions are expressions that are written differently but have the same value. Let’s look at an example…

Write an expression that is equivalent to **2 (3 + n)**.

We can use our knowledge of multiplication to recognize that **2** times **3 + n** is the same as saying **2** groups of **3 + n**.

We can represent the two groups with a model.

We can see by looking at the model that the expression could be written as

6 + 2n

We can check our answer with the **distributive property**.

2 (3 + n)

When using the distributive property, we distribute the **2** to each term within the

parenthesis. Doing this allows us to forgo the order of operations, which comes in

handy when we are working with variables.

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Use a model to illustrate **4(2 + p)**.

Answers may vary

Use a model to illustrate **3(x + 4)**.

Answers may vary

Combine like terms to find an equivalent expression for **2t + 4 + 3t – 2**.

5t + 2

Combine 2t and 3t. Then combine 4 – 2.

Combine like terms to find an equivalent expression for **3y + 2t – t + 2y**.

5y + t

Combine 3y + 2y. Then combine 2t – t.

Combine like terms to find an equivalent expression for **4s + 1 – s**.

3s + 1

Combine 4s – s

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