To simplify the expression \( 4(34x + 3x - 2) - 2(3x^2 + 1 + 3x) \), we'll distribute and then combine like terms.
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Distribute \( 4 \) in the first part: \[ 4(34x + 3x - 2) = 4(34x) + 4(3x) - 4(2) = 136x + 12x - 8 = 148x - 8 \]
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Distribute \( -2 \) in the second part: \[ -2(3x^2 + 1 + 3x) = -2(3x^2) - 2(1) - 2(3x) = -6x^2 - 2 - 6x \]
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Now combine the two results: \[ (148x - 8) + (-6x^2 - 2 - 6x) = -6x^2 + 148x - 6x - 8 - 2 \]
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Combine like terms: \[ -6x^2 + (148x - 6x) + (-8 - 2) = -6x^2 + 142x - 10 \]
Thus, the expression simplifies to: \[ -6x^2 + 142x - 10 \]
This is the equivalent expression with the fewest terms possible.
If you prefer to present it in standard form, you can write it as: \[ -6x^2 + 142x - 10 \]
Where we may leave it in that format or ask for additional reductions based on specific goals.
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