# Lesson 5 Homework Practice Algebra Properties Answers To The Impossible Quiz

In algebra simplifying expressions is an important part of the process. Use this lesson to help you simplify algebraic expressions.

### Simplifying expressions

Simplifying an expression is just another way to say **solving a math problem**. When you **simplify** an expression, you're basically trying to write it in the **simplest** way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression:

4 + 6 + 5

If you **simplified** it by combining the terms until there was nothing left to do, the expression would look like this:

15

In other words, 15 is the **simplest** way to write 4 + 6 + 5. Both versions of the expression equal the exact same amount; one is just much shorter.

Simplifying **algebraic expressions** is the same idea, except you have variables (or letters) in your expression. Basically, you're turning a long expression into something you can easily make sense of. So an expression like this...

(13x + -3x) / 2

...could be simplified like this:

5x

If this seems like a big leap, don't worry! All you need to simplify most expressions is basic arithmetic -- addition, subtraction, multiplication, and division -- and the order of operations.

#### The order of operations

Like with any problem, you'll need to follow the** order of operations **when simplifying an algebraic expression. The order of operations is a rule that tells you the correct **order** for performing calculations. According to the order of operations, you should solve the problem in this order:

- Parentheses
- Exponents
- Multiplication and division
- Addition and subtraction

Let's look at a problem to see how this works.

In this equation, you'd start by simplifying the part of the expression in **parentheses**: 24 - 20.

2 ⋅ (24 - 20)^{2} + 18 / 6 - 30

**24** minus **20** is 4. According to the order of operations, next we'll simplify any **exponents**. There's one exponent in this equation: 4^{2}, or **four to the second power**.

2 ⋅ 4^{2} + 18 / 6 - 30

**4 ^{2}**is 16. Next, we need to take care of the

**multiplication**and

**division**. We'll do those from left to right: 2 ⋅ 16 and 18 / 6.

2 ⋅ 16 + 18 / 6 - 30

**2 ⋅ 16** is 32, and **18 / 6** is 3. All that's left is the last step in the order of operations: **addition** and **subtraction**.

32 + 3 - 30

**32 + 3** is 35, and **35 - 30** is 5.** Our expression has been simplified—there's nothing left to do.**

5

That's all it takes! Remember, you **must** follow the order of operations when you're performing calculations—otherwise, you may not get the correct answer.

Still a little confused or need more practice? We wrote an entire lesson on the order of operations. You can check it out here.

#### Adding like variables

To add variables that are the same, you can simply **add the coefficients**. So** 3 x + 6x** is equal to 9

*x*. Subtraction works the same way, so

**5**1

*y*- 4*y*=*y*, or just

*y*.

5y - 4y = 1y

You can also **multiply** and **divide** variables with coefficients. To multiply variables with coefficients, first multiply the coefficients, then write the variables next to each other. So **3 x ⋅ 4y** is 12

*xy*.

3x ⋅ 4y = 12xy

#### The Distributive Property

Sometimes when simplifying expressions, you might see something like this:

3(x+7)-5

Normally with the Order of Operations, we would simplify what is **inside** the parentheses first. In this case, however, x+7 can't be simplified since we can't add a variable and a number. So what's our first step?

As you might remember, the 3 on the outside of the parentheses means that we need to multiply everything **inside** the parentheses by 3. There are **two** things inside the parentheses: **x** and **7**. We'll need to multiply them **both** by 3.

3(x) + 3(7) - 5

3 · x is **3x** and 3 · 7 is **21**. We can rewrite the expression as:

3x + 21 - 5

Next, we can simplify the subtraction 21 - 5. 21 - 5 is **16**.

3x + 16

Since it's impossible to add variables and numbers, we can't simplify this expression any further. Our answer is **3x + 16**. In other words, 3(x+7) - 5 = 3x+16.

### Assessment

Want even more practice? Try out a short assessment to test your skills by clicking the link below:

Start Assessment

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