IXL | Identify equivalent expressions

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or

Learn with an example

question

Which expression is equivalent to

2

(

f

+

6

)

?

12

f

(

f

+

6

)

2

6

(

f

+

2

)

12

f

+

2

key idea

Two expressions are equivalent if they are the same when written in standard form.

For example,

3

(

x

+

4

)

and

2

x

+

x

+

12

are equivalent because they have the same standard form,

3

x

+

12

.

solution

To find which expression is equivalent to

2

(

f

+

6

)

,

write each one in standard form. See which expression has the same standard form as

2

(

f

+

6

)

.

First, write

2

(

f

+

6

)

in standard form.

2

(

f

+

6

)

=

Apply the distributive property

2

f

+

12

Apply the distributive property

The standard form of

2

(

f

+

6

)

is

2

f

+

12

.

The expression

12

f

is already in standard form, but the standard form of

2

(

f

+

6

)

is

2

f

+

12

.

12

f

and

2

(

f

+

6

)

are not

equivalent.

Write

(

f

+

6

)

2

in standard form.

(

f

+

6

)

2

=

Apply the distributive property

2

f

+

12

Apply the distributive property

The standard form of

(

f

+

6

)

2

is

2

f

+

12

,

and the standard form of

2

(

f

+

6

)

is also

2

f

+

12

.

(

f

+

6

)

2

and

2

(

f

+

6

)

are

equivalent.

Write

6

(

f

+

2

)

in standard form.

6

(

f

+

2

)

=

Apply the distributive property

6

f

+

12

Apply the distributive property

The standard form of

6

(

f

+

2

)

is

6

f

+

12

,

but the standard form of

2

(

f

+

6

)

is

2

f

+

12

.

6

(

f

+

2

)

and

2

(

f

+

6

)

are not

equivalent.

The expression

12

f

+

2

is already in standard form, but the standard form of

2

(

f

+

6

)

is

2

f

+

12

.

12

f

+

2

and

2

(

f

+

6

)

are not

equivalent.

The correct answer is

(

f

+

6

)

2

.

Looking for more? Try these:

Lesson: Equivalent expressions

or

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