Which expression is equivalent to 60(14x−2)+20(34y−4)

Question

(1 point)
Responses

30xy−200
30 x y minus 200

15x+15y−64
15 x plus 15 y minus 64

15x−15y−200
15 x minus 15 y minus 200

15x+15y−200

Answer 1

To simplify the expression \( 60(14x - 2) + 20(34y - 4) \), follow these steps:

1. Distribute \( 60 \) in the first term: \[ 60(14x - 2) = 60 \cdot 14x - 60 \cdot 2 = 840x - 120 \]

2. Distribute \( 20 \) in the second term: \[ 20(34y - 4) = 20 \cdot 34y - 20 \cdot 4 = 680y - 80 \]

3. Combine the results: \[ 840x - 120 + 680y - 80 \]

4. Combine like terms: \[ 840x + 680y - 120 - 80 = 840x + 680y - 200 \]

So the simplified expression is: \[ 840x + 680y - 200 \]

Now, looking at the response options, we can factor out common terms.

Notice that: \[ 840x + 680y - 200 = 60(14x) + 20(34y) - (120 + 80) = 60(14x) + 20(34y) - 200 \]

The closest expression that matches is \( 15x + 15y - 200 \). To see why this is, we'll factor out common coefficients.

Thus, the correct answer is: \[ 15x + 15y - 200 \]

This term corresponds to the answer option: 15x + 15y - 200.