4xy(1/2y+3/2x)= ?

a. 2x + 6y
b. 2x + 12y
c. 4x + 6y
d. 4x + 12y
e. 4x - 12y

please answer and explain

yes,4xy(1/(2y) + 3/(2x) )

thank you

1/(2y) + 3/(2x) = x/(2xy) + 3y/(2xy) = (x+3y)/(2xy)

and now it's easy, eh?

To simplify the given expression, we need to distribute the values inside the parentheses to each term.

We start by multiplying 4xy with 1/2y:
4xy * 1/2y = (4/1 * x/1 * y/1) * (1/2 * y/1) = (4x * y) / (1 * 2) = (4xy) / 2 = 2xy.

Next, let's multiply 4xy with 3/2x:
4xy * 3/2x = (4/1 * x/1 * y/1) * (3/2 * x/1) = (4x * y) / (1 * 2) * (3/1 * x/1) = (4xy * 3x) / (2 * 1) = 12x^2y / 2 = 6x^2y.

Now we have: 2xy + 6x^2y.

Looking at the answer choices:
a) 2x + 6y does not match the simplified expression.
b) 2x + 12y does not match the simplified expression.
c) 4x + 6y does not match the simplified expression.
d) 4x + 12y does not match the simplified expression.
e) 4x - 12y does not match the simplified expression.

None of the answer choices match the simplified expression 2xy + 6x^2y. Therefore, none of the provided answer choices are correct.

4xy(1/2y + 3/2x)

= 4xy( (y+3x)/2 )
= 2xy(y+3x)
= 2xy^2 + 6x^2y

none of the choices
I suspect a typo

did you mean
4xy(1/(2y) + 3/(2x) ) ?
then
= 4xy( (x + 3)/(2xy) )
= 2(x + 3y)
= 2x + 6y

looks like you did have a typo.