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Select each expression that is equivalent to 3(n+6) . Select all that apply.
A. 3n+6
B. 3n+18
C. 2n+2+n+4
D. 2(n+6)+(n+6)
E. 2(n+6)+n

Respuesta :

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ANSWER

B. 3n+18

D. 2(n+6)+(n+6)



EXPLANATION

The given expression is

[tex]3(n + 6)[/tex]


We expand the bracket using the distributive property to obtain,


[tex] = 3n + 18[/tex]

This will give us option B as one of the correct answers.


We could also rewrite

[tex]3(n + 6) = 2(n + 6) + 1(n + 6)[/tex]



This will give us


[tex]3(n + 6) = 2(n + 6) + (n + 6)[/tex]


Hence option D is another correct answer.

To solve the problem we must know about like terms.

What are Like terms?

like terms are those terms that are having the same variables, also the variables are of the same order as well.

for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.

Given to us

  • Desired Expression = 3(n+6)

A.)  3n+6

       Taking 3 as a common factor,

       = 3(n+2)

As we can see the expression is not equal to 3(n+6), when solved. therefore, it is not the desired expression.

B.)  3n+18

       Taking 3 as a common factor,

        = 3(n+6)

As we can see the expression is equal to 3(n+6) when solved. therefore, it is the desired expression.

C.)  2n+2+n+4

       = 3n+6

       Taking 3 as a common factor,

       = 3(n+2)

As we can see the expression is not equal to 3(n+6), when solved. therefore, it is not the desired expression.

D.)  2(n+6)+(n+6)

       = 2n+12+n+6

       = 3n+18

       Taking 3 as a common factor,

       =3(n+6)

As we can see the expression is equal to 3(n+6) when solved. therefore, it is the desired expression.

E.)  2(n+6)+n

       = 2n + 12 + n

       = 3n + 12

       Taking 3 as a common factor,

       = 3(n+4)

as we can see the expression is not equal to 3(n+6), when solved. therefore, it is not the desired expression.

Learn more about Like Terms:

https://brainly.com/question/2513478

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