To simplify the expression \( 60(14x - 2) + 20(34y - 4) \), we will first distribute the constants \( 60 \) and \( 20 \) into the parentheses.
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Distributing \( 60 \): \[ 60(14x) - 60(2) = 840x - 120 \]
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Distributing \( 20 \): \[ 20(34y) - 20(4) = 680y - 80 \]
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Now combine the two results: \[ 840x - 120 + 680y - 80 \]
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Combine like terms: \[ 840x + 680y - 200 \]
Thus, the expression simplifies to: \[ 840x + 680y - 200 \]
Now, we can see if this matches any of the given responses. However, the responses do not appear to directly reflect that long-form expression.
To express this result in a manner that corresponds to given options, we can inspect for any common factors:
- \( 840x + 680y - 200 \) can be factored or simplified more, but it appears none of the options align with that direct outcome.
However, I will focus on the potential responses given:
- None of these provided options seem initially comparable to the simplified expression we derived.
To see if there was any oversight in the matching with the response options, we may need more clarity. Each response given involves smaller terms and potentially indicates there might have been a reductions/transfer step in interpreting them as polynomial or in special formats.
If selecting from your listed options based on original simplifications will be optimal, lean towards approaching any expressed format extending from the initial operation to perhaps form theoretical ratios/sections overall relative simplifications.
So, after an analysis, it appears that none of the options provided seems equivalent or accurately fall directly from this initial compiled equation;
The closest drifting outcomes may target background functions yet mentioned but cannot decisively map.
Nonetheless, it might be worthwhile double-checking the response matrix for any amendments or comparatives as is.