High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Request a demo

In order to access this I need to be confident with:

Add and subtract within 100

Integers Algebraic expression

Algebraic notation

Combining like terms

Math resources Algebra Algebraic Expressions

Simplifying Expressions

Simplifying expressions

Here you will learn about simplifying expressions, including using the distributive property and combining like terms.

Students will first learn about simplifying expressions as part of expressions and equations in 6th grade.

What is simplifying expressions?

Simplifying expressions involves using the properties of operations to create equivalent algebraic expressions.

For example,

Simplify $4(x+7)-x.$

First, look at $4(x+7)$ which is $‘4$ times the sum of $x$ and $7.’$

Notice that each method shows $4(x+7)=4x+28.$

Since $4(x+7)-x=4x+28-x,$ you can continue to simplify by combining the like terms, in this case the $x$ s.

Use the commutative property to change the order:

$4x+28-x=4x-x+28$

Next, let’s simplify the $4x-x$ .

Visually, if you have $4$ positive $x$ ‘s and we subtract an $x,$ you are left with $3$ positive $x$ ‘s:

So, $4x-x=3x.$

This means that $4x+28-x$ can be simplified to $3x+28.$

You cannot simplify any further because $‘3x’$ and $‘+28’$ are not like terms. One has the variable $x,$ and the other is a constant.

What is simplifying expressions?

Common Core State Standards

How does this relate to 6th grade math?

Grade 6 – Expressions and Equations (6.EE.A.3)
Apply the properties of operations to generate equivalent expressions.
For example, apply the distributive property to the expression $3 \, (2 + x)$ to produce the equivalent expression $6 + 3x;$ apply the distributive property to the expression $24x + 18y$ to produce the equivalent expression $\, 6 (4x + 3y);$ apply properties of operations to $y + y + y$ to produce the equivalent expression $3y.$

[FREE] Simplifying Expressions Worksheet (Grade 6)

Use this worksheet to check your 6th grade students’ understanding of simplifying expressions. 15 questions with answers to easily identify areas of strength and support!

DOWNLOAD FREE

[FREE] Simplifying Expressions Worksheet (Grade 6)

Use this worksheet to check your 6th grade students’ understanding of simplifying expressions. 15 questions with answers to easily identify areas of strength and support!

DOWNLOAD FREE

How to simplify expressions

In order to simplify expressions:

Multiply the terms within the parentheses by the term on the outside.
Combine like terms.
Write the simplified expression.

Simplifying expressions examples

Example 1: simplify in one-step

Simplify $3 \, (5 + p).$

Multiply the terms within the parentheses by the term on the outside.

$3 \, (5 + p)$ is $‘3$ times the sum of $5$ and $p.’$

There are $3$ different ways to solve:

Notice that each method shows $3 \, (5 + p) = 15 + 3p.$

2Combine like terms.

You cannot simplify any further because $‘+3p’$ and $‘15’’$ are not like terms. One has the variable $p,$ and the other is a constant.

3Write the simplified expression.

$3 \, (5 + p)$ simplified is $15 + 3p.$

Example 2: simplify in two-steps

Simplify $2 \, (2m + 6) + 1.$

Multiply the terms within the parentheses by the term on the outside.

$2 \, (2m + 6)$ is $‘2$ times the sum of $2m$ and $6.’$

There are $3$ different ways to solve:

Combine like terms.

You can simplify further because $‘+12’$ and $‘+1’$ are like terms: $12 + 1 = 13.$

Write the simplified expression.

$2 \, (2m + 6) + 1$ simplified is $4m + 13.$

Example 3: simplify in one-step

Simplify $4 \, (8-k) + 3k.$

Multiply the terms within the parentheses by the term on the outside.

$4 \, (8-k)$ is $‘4$ times the difference of $8$ and $k.’$

There are $3$ different ways to solve:

Simplifying Expressions example 3 image 1

Combine like terms.

Since $‘-4k’$ and $‘+3k’$ are like terms, you can simplify further and combine them: $-4k + 3k.$

Visually if you have $4$ negative $ks$ and $3$ positive $ks,$ each negative and positive create a zero pair, leaving $1$ negative $k$ :

So, $-4k + 3k = -k.$

Write the simplified expression.

$4 \, (8-k) + 3k$ simplified is $32-k.$

Example 4: simplify two-steps with the distributive property

Simplify $9 \, (1 + 2y) - 5y.$

Multiply the terms within the parentheses by the term on the outside.

$9 \, (1 + 2y)$ is $‘9$ times the sum of $1$ and $2y.’$

Distribute the $9$ to the $1$ and the $+2y.$

So, $9 \, (1 + 2y)-5y = 9 + 18y-5y.$

Combine like terms.

You can simplify further because $‘+18y’$ and $‘-5y’$ are like terms: $18y-5y.$

Visually if you have $18$ positive $y$ s and then subtract $5 \, y$ s, there are $13$ positive $y$ s left:

Simplifying Expressions example 4 image 2

So, $18y-5y = 13y.$

Write the simplified expression.

$9 \, (1 + 2y)-5y$ simplified is $9 + 13y.$

Example 5: simplify two-steps with two variables with the distributive property

Simplify $7 \, (h + 4t)-9t.$

Multiply the terms within the parentheses by the term on the outside.

$7 \, (h + 4t)$ is $‘7$ times the sum of $h$ and $+4t.’$

Distribute the $7$ to the $h$ and the $4t.$

So, $7\, (h + 4t)-9t = 7h + 28t-9t.$

Combine like terms.

You can simplify further because $‘+28t’$ and $‘-9t’$ are like terms: $28t-9t = 19t.$

Write the simplified expression.

$7 \, (h + 4t)-9t$ simplified is $7h + 19t.$

Example 6: perimeter multi-step with distributive property

Write the simplified expression for the perimeter of the shape.

Multiply the terms within the parentheses by the term on the outside.

The perimeter of the rectangle is $2l + 2w = 2 \, (x-2) + 2 \, (2x + 3).$

$\hspace{1.5cm} 2 \, (x-2) \hspace{2cm} + \hspace{2cm} 2 \, (2x + 3)$

$\hspace{0.8cm} 2 \, (x-2)$ is $‘2$ times $\hspace{3cm} 2 \, (2x + 3)$ is $‘2$ times

$\hspace{0.3cm}$ the difference of $x$ and $2.’ \hspace{2.8cm}$ the sum of $2x$ and $3.’$

Distribute the $2$ to the $x$ and the $-2. \hspace{0.8cm}$ Distribute the $2$ to the $2x$ and the $3.$

Simplifying Expressions example 6 image 2

So, $2 \, (x-2) + 2 \, (2x + 3) = 2x-4 + 4x + 6.$

Combine like terms.

You can simplify further because $‘+2x’$ and $‘+4x’$ are like terms: $2x + 4x = 6x.$

$‘-4’$ and $‘6’$ are also like terms: $-4 + 6.$

Visually if you have $4$ negatives and add $6$ positives, each negative and positive create a zero pair, leaving $2$ positives:

So, $-4 + 6 = 2.$

Write the simplified expression.

$2 \, (x-2) + 2 \, (2x + 3)$ simplified is $6x + 2.$

[FREE] Simplifying Expressions Worksheet (Grade 6)

Use this worksheet to check your 6th grade students’ understanding of simplifying expressions. 15 questions with answers to easily identify areas of strength and support!

DOWNLOAD FREE

[FREE] Simplifying Expressions Worksheet (Grade 6)

Use this worksheet to check your 6th grade students’ understanding of simplifying expressions. 15 questions with answers to easily identify areas of strength and support!

DOWNLOAD FREE

Teaching tips for simplifying expressions

Before students can simplify an algebraic expression, they need to understand exactly what makes up the expression. Encourage students to model expressions that have variables with hands-on manipulatives (such as algebra tiles), digital resources or their own drawings before beginning to simplify.

Even if students have not learned how to operate with integers, they can still be successful at simplifying expressions like these. Encourage students to use what they know about positive and negative numbers and support their understanding with models, like those shown on this page.

Easy mistakes to make

Confusing the order of operations (pemdas) when simplifying algebraic expressions
Expressions should always be simplified following the order of operations. For most simple expressions, that means simplifying the parentheses using the distributive property and then adding the like terms from left to right. Doing this out of order, leads to the incorrect answer.

For example,
Simplify $7 \, (x +1)-4x +2x…$

Thinking the original expression and simplified are not equivalent
Just like simplified fractions are equivalent versions of the original fractions, the same is true for simplified algebraic expressions. Using the distributive property and combining like terms does not change the value of the expression.

Not including a positive or negative sign
When combining the like terms, you must include the sign in front of the term.
For example,
$5h + 8p-3h$ simplified is $2h + 8p.$
To combine the like $h$ terms, solve $5h-3h.$ The subtraction or negative sign stays with the $3h.$ And the addition or positive sign stays with the $8h.$

Terms with a coefficient of $\bf{1}$
For terms with a coefficient of $1,$ you don’t need to write the $1.$
For example,

$1x=x \hspace{0.6cm} 1y+ 4m=y + 4m \hspace{0.6cm} 6 \, (4 + 1r) = 6 \, (4 + r)$

Forgetting to use parentheses
When multiplying an expression by a value, use parentheses so that each term is multiplied. Not using parentheses changes the outcome.
For example,

$2 \, (y+4) = 2y + 8 \hspace{1.3cm} 2 \times y+4=2 y+4$

Practice simplifying expressions questions

4d + 10

4d + 40

44d

4 + d + 10

$4 \, (d + 10)$ is $‘4$ times the sum of $d$ and $10.’$

There are $3$ different ways to solve:

Simplifying Expressions prac question 1

5f + 3

8f

5f + 1

3-f

Simplify the parentheses first.

$3 \, (1 + 3f)$ is $‘3$ times the sum of $1$ and $3f.’$

There are $3$ different ways to solve:

Simplifying Expressions prac question 2 image 1

You can simplify further because $‘+9f’$ and $‘-4f’$ are like terms: $9f-4f.$

Visually if you have $9$ positive $f$ s and then subtract $4 \, f$ s, there are $5$ positive $f$ s left:

So, $9f-4f = 5f.$

$3 \, (1 + 3f)-4f$ simplified is $5f + 3.$

*Remember, because of the commutative property $3 + 5f = 5f + 3.$

3x

11x-4

3x-4

11x-8

Simplify the parentheses first.

$2 \, (x-4)$ is $‘2$ times the difference of $x$ and $4.’$

There are $3$ different ways to solve:

Simplifying Expressions US image 1

You can simplify further because $‘2x’$ and $‘+9x’$ are like terms: $2x + 9x.$

Visually if you have $2$ positive $x$ s and then add $9 \, x$ s, there are $11$ positive $x$ s left:

So, $2x + 9x = 11x.$

$2 \, (x-4) + 9x$ simplified is $11x-8.$

36m

24m + 23

24m + 12

66m-30

Simplify the parentheses first.

$6 \, (4m + 7)$ is $‘6$ times the sum of $4m$ and $7.’$

Distribute the $6$ to the $4m$ and the $7.$

Simplifying Expressions prac question 4

So, $6 \, (4m + 7)-30 = 24m + 42-30.$

You can simplify further because $‘+42’$ and $‘-30’$ are like terms: $42-30 = 12.$

$6 \, (4m + 7)-30$ simplified is $24m + 12.$

11n + 7b

18nb

11n-13b

11b + 7n

Simplify the parentheses first.

$11 \, (n + 2b)$ is $‘11$ times the sum of $n$ and $2b.’$

Distribute the $11$ to the $n$ and the $2b.$

Simplifying Expressions prac question 5

So, $11 \, (n + 2b)-15b = 11n + 22b-15b$

You can simplify further because $‘+22b’$ and $‘-15b’$ are like terms: $22b-15b = 7b.$

$11 \, (n + 2b)-15b$ simplified is $11n + 7b.$

8x+22

6x+14

4x+11

4x^{2}+22x+30

To calculate the perimeter, add all side lengths together by combining the like terms.

Simplifying Expressions prac question 6 image 2

The simplified expression for the perimeter is $8x + 22.$

Simplifying expressions FAQs

Is there a way to undo the simplification of an expression?

Yes, you can use factoring to reverse the distributive property.

Can other types of algebraic expressions be simplified?

Yes, in 7th grade, students will learn to simplify rational expressions that are equal to linear equations, including fractions with variables in the numerator and/or the denominator and expressions.

In 8th grade, students will expand on this knowledge by including variables with exponents and continuing into high school, where algebraic expressions are simplified within inequalities.

Can the distributive property be used only with multiplication?

No, the distributive property can be used with multiplication and division. For example,

$55 \div 5$
$=(45+10) \div 5$
$=45 \div 5+10 \div 5$
$=9+2$
$=11$

The next lessons are

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.