Question

Which expression is equivalent to 30(12x−2)+40(34y−4)
(1 point)
Responses

15x+30y−64
15 x plus 30 y minus 64

45xy−220
45 x y minus 220

15x−30y−220
15 x minus 30 y minus 220

15x+30y−220

Answer 1

To simplify the expression \(30(12x−2)+40(34y−4)\), we can distribute the terms:

1. Distribute \(30\) in \(30(12x - 2)\):
\[
30 \times 12x - 30 \times 2 = 360x - 60
\]

2. Distribute \(40\) in \(40(34y - 4)\):
\[
40 \times 34y - 40 \times 4 = 1360y - 160
\]

Now combine the results from both distributions:
\[
360x - 60 + 1360y - 160
\]

Now simplify by combining like terms:
1. The \(x\) term is \(360x\).
2. The \(y\) term is \(1360y\).
3. The constant terms are \(-60 - 160 = -220\).

Putting it all together, we have:
\[
360x + 1360y - 220
\]

None of the response options you provided exactly match this expression. It seems that the equivalent expression might not be listed, or there is a misunderstanging in the context given.

However, strictly following your given options, \(15x + 30y - 220\) seems the closest in the constant term but the coefficients of x and y seem off.

If there was a typo, please recheck the options, else the correct answer from simplification is:
\[
360x + 1360y - 220
\]