Question

An expression is shown below.

Which expression is an equivalent expression?

Please work it out to show how you got the answer.

Answer 1

C

Step-by-step explanation (A):

`(4)/(5)(3x+5y)`

Apply the Distributive Property

`(4)/(5)*3x+(4)/(5)*5y`

Cross out the common factor

`(4)/(5)*3x+4y`

Multiply the monomials

`(12)/(5)x+4y`

Determine true/false

`Determine\ whether\ (12)/(5)x+(20)/(3)y\ and\\ (4)/(5)(3x+5y)\ are\ equivalent\\ False`

Step-by-step explanation (B):

`(4)/(15)(3x-5y)`

Apply the Distributive Property

`(4)/(15)*3x-(4)/(15)*5y`

Cross out the common factor

`(4)/(5)x-(4)/(15)*5y\\ (4)/(5)*-(4)/(3)y`

Determine true/false

`Determine\ whether\ (12)/(5)x+(20)/(3)y\ and\ (4)/(15)(3x-5y)\ are\ equivalent:`

`False`

Step-by-step explanation (C):

`(4)/(15)(9x+25y)`

Apply the Distributive Property

`(4)/(15)*9x+(4)/(15)*25y`

Cross out the common factor

`(4)/(5)*3x+(4)/(15)*25y\\ (4)/(5)*3x+(4)/(3)*5y`

Multiply the monomials

`(12)/(5)x+(4)/(3)*5y\\ (12)/(5)x+(20)/(3)y`

Determine true/false

`Determine\ whether\ (12)/(5)x+(20)/(3)y\ and\ (4)/(15)(9x+25y)\ are\ equivalent:\\ True`

Step-by-step explanation (D):

`(4)/(3)(3x-5y)`

Apply the Distributive Property

`(4)/(3)*3x-(4)/(3)*5y`

Cross out the common factor

`4x-(4)/(3)*5y`

Multiply the monomials

`4x-(20)/(3)y`

Determine true/false

`Determine\ whether\ (12)/(5)x+(20)/(3)y\ and\ (4)/(3)(3x-5y)\ are\ equivalent:\\ False`

I hope this helps you

:)