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Order of operationsAdding and subtracting negative numbers

Multiplying and dividing negative numbers

Here you will learn how to expand expressions before simplifying the resulting algebraic expressions.

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

Expanding expressions (or multiplying out) is the process by which you use the distributive property to remove parentheses from an algebraic expression.

To do this, you need to multiply out the parentheses by multiplying everything outside of the parentheses by everything inside the parentheses. Then, if needed, you simplify the resulting expression by combining the like terms.

For example,

2(x+5) = 2x+10

For this example,

The expression has two sets of parentheses. You will need to simplify by combining like terms after expanding the expression.

\begin{aligned} & 2(x+5)+3(x-1) \\\\ & =2 x+10+3 x-3 \\\\ & =5 x+7 \end{aligned}

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 .

In order to expand expressions:

**Use the distributive property to “multiply out” the parentheses in the expression.****Combine the like terms.**

Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

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9 \, (y+6)

**Use the distributive property to “multiply out” the parentheses in the expression.**

\begin{aligned} & 9 \, (y+6) \\\\ & =(9 \times y)+(9 \times 6) \\\\ & =9 y+54 \end{aligned}

2**Combine the like terms.**

There are no like terms in the expression, so you are finished.

The expanded expression is 9y+54 .

Expand and simplify:

6 \, (𝑡 + 8)–12

**Use the distributive property to “multiply out” the parentheses in the expression.**

\begin{aligned} & 6 \, (t+8)-12 \\\\ & =(6 \times t)+(6 \times 8)-12 \\\\ & =6 t+48-12 \end{aligned}

**Combine the like terms.**

6 t+48-12

= 6t+36

So the expanded and simplified expression is 6t+36 .

5 b+7(b-2)-18

**Use the distributive property to “multiply out” the parentheses in the expression.**

\begin{aligned} & 5 b+7(b-2)-18 \\\\ & =5 b+(7 \times b)-(7 \times 2)-18 \\\\ & =5 b+7 b-14-18 \end{aligned}

**Combine the like terms.**

\begin{aligned} & 5 b+7 b-14-18 \\\\ & =12 b-32 \end{aligned}

So the expanded and simplified expression is 12b-32 .

Expand and simplify:

8(x-2)+6(x+3)

**Use the distributive property to “multiply out” the parentheses in the expression.**

Multiply out the first set of parentheses.

\begin{aligned} & 8 \, (x-2) \\\\ & =(8 \times x)-(8 \times 2) \\\\ & =8 x-16 \end{aligned}

The first set of parentheses expands to 8x–16 .

\begin{aligned} & 6 \, (x+3) \\\\ & =(6 \times x)+(6 \times 3) \\\\ & =6 x+18 \end{aligned}

The second set of parentheses expands to 6x + 18 .

The expression is now,

8 x-16+6 x+18

**Combine the like terms.**

First, use the commutative property to group the like terms together.

Underline the two x terms (8x and +6x) and combine them. Then do the same for the two constants (-16 and +18). Remember to underline the sign in front of the number too!

8 x+6 x=14 x

-16 and +18 = 2

(Note that -16 + 18 can also be written as 18-16 ).

So the expanded and simplified expression is 14x + 2 .

Expand and simplify:

2 x(x+6)-3(x-2)

**Use the distributive property to “multiply out” the parentheses in the expression.**

Multiply out the first set of parentheses.

\begin{aligned} & 2 x \, (x+6) \\\\ & =(2 x \times x)+(2 x \times 6) \\\\ & =2 x^2+12 x \end{aligned}

The first set of parentheses expands to 2x^2 + 12x .

Multiply out the second set of parentheses.

\begin{aligned} & -3 \, (x-2) \\\\ & =(-3 \times x)+(-3 \times 2) \end{aligned}

*Note: since the minus sign stays with the 3 to become negative 3, you will now add the products.

=-3 x+6

The second set of parentheses expands to –3x + 6 .

The expression is now,

2 x^2+12 x-3 x+6

**Combine the like terms.**

The first term will be 2x^2 since there are no other exponents. Underline the two x terms (12x and -3x) and combine them.

Remember to underline the sign in front of the number too. Since there is only one constant, the expression will end in +6.

12 x-3 x=9 x

The expanded and simplified expression is 2x^2 + 9x + 6 .

Expand and simplify:

3 \, (2 x-6 y)-5 \, (x-2 y)

**Use the distributive property to “multiply out” the parentheses in the expression.**

Multiply the first set of parentheses. Another method you can use is to write the terms in an area model:

(A positive number times a negative number equals a negative number so 3 \times -6y gives a negative answer. You need to write -18y ).

The first set of parentheses expands to 6x–18y .

Multiply out the second set of parentheses. Remember, you are multiplying both x and -2y by -5 .

(A negative number times a negative number equals a positive number so -5 \times -2y gives a positive answer. You need to write +10y ).

The second set of parentheses expands to –5x + 10y .

The expression is now,

6 x-18 y-5 x+10 y

**Combine the like terms.**

Underline the two x terms (6x and -5x) and the two y terms (-18y and +10y).

Remember to underline the sign in front of the number too.

The expanded and simplified expression is x-8y .

- Assess students’ prior knowledge before beginning. Review key vocabulary terms including algebraic expression, parentheses, simplify, exponents, distributive property, binomial, polynomial, terms, coefficients. Review adding and subtracting negative numbers as needed.

- Allowing learners to use templates or organizers when practicing this skill or completing worksheets, such as the area model shown above, will help them organize their work as they complete the process step-by-step.

- Be sure students have had plenty of practice expanding expressions with one set of parentheses before moving on to expanding expressions with binomials or polynomials.

- The expanding expression tool kit you will provide students is essential for higher levels of mathematics.

**Multiplying all terms in the set of parentheses**

You must__multiply__the term outside the parentheses by__every term__inside the parentheses.

For example,

2\left(6 x^2-3 x\right)=12 x^2-3 x

Here, you have not multiplied the value outside of the parentheses by the second term. The correct answer is:

2\left(6 x^2-3 x\right)=12 x^2-6 x

**Squaring a term**

When you square something, you multiply it by itself.

For example,

\begin{aligned} 3^{2}&=3\times 3\\ x^{2}&=x\times x\\ (5y)^{2}&=5y\times 5y \end{aligned}

**Combining like terms**

When you combine like terms, you must include the sign in front of the number. Be sure to underline the sign along with the number when combining the like terms.

For example,

1. Expand and simplify:

5 \, (m+9)-4 m

5m+9

m+9

9m+45

m+45

Expand each set of parentheses:

5m + 45-4m

Combine like terms:

m+45

2. Expand and simplify:

4 h-2(h+8)-1

2h-17

2h+17

2h-5

h-15

Expand each set of parentheses:

4h-2h-16-1

Combine like terms:

2h-17

3. Expand and simplify:

3 \, (x+7)-2 \, (x+3)

5x+15

x+15

x+27

5x+27

Expand each set of parentheses:

3x + 21-2x-6

Combine like terms:

x+15

4. Expand and simplify:

8 \, (y-5)+5 \, (y-2)

13y-30

3y-50

13y-50

3y-30

Expand each set of parentheses:

8y-40 + 5y-10

Combine like terms:

13y-50

5. Expand and simplify:

5 x \, (3 x-2)-4 x \, (2 x+3)

23x^2-22x

7x^2-5

7x^2-22x

7x^2-2x

Expand each set of parentheses:

15x^{2}-10x-8x^{2}-12x

Combine like terms:

7x^{2}-22x

6. Expand and simplify:

5 \, (6 x-2 y)-2 \, (8 x-5 y)

14x

14x-20y

46x

14x+20y

Expand each set of parentheses:

30x-10y-16x+10y

Combine like terms:

14x

To expand an expression, you need to multiply out the parentheses by multiplying everything outside of the parentheses by everything inside of the parentheses. Then, if needed, you simplify the resulting expression by combining the like terms.

Combine like terms by first identifying the like terms, then adding them together using the value of their coefficients.

Expanding expressions are useful when solving and graphing quadratic equations, rational expressions, and solving non-linear simultaneous equations.

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[FREE] Common Core Practice Tests (Grades 3 to 6)

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Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!