Write 2 equivalent expressions for this expression. and explain how you arrived at the equivalent expressions by showing all your steps and stating which properties you used.

3(3j + 7 + j)

best answer will be !

The equivalent expression is 12j + 21 and 3(4j + 7)

Solution:

Given that we have to write 2 equivalent expression

Given expression is:

3(3j + 7 + j)

Combine the like terms. Combine 3j and j we get 4j

Thus the expression becomes,

3(4j + 7)

Now let us use distributive property

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

The distributive property is represented as:

a(b + c) = ab + ac

Apply distributive property in 3(4j + 7)

Thus one of the equivalent expression is 12j + 21

Second equivalent expression:

From first equivalent expression,

12j + 21

Factor out the greatest common factor

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 21 are: 1, 3, 7, 21  

Then the greatest common factor is 3

Thus factor out 3 from 12j + 21

Thus the another equivalent expression is 3(4j + 7)

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

a

step-by-step explanation: