To add the given expressions, we will combine like terms.
Expression 1:
\[ -3k + 4k^3 - 2 - 3k + 4k^3 - 2 \]
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Combine the \( k^3 \) terms: \[ 4k^3 + 4k^3 = 8k^3 \]
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Combine the \( k \) terms: \[ -3k - 3k = -6k \]
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Combine the constant terms: \[ -2 - 2 = -4 \]
So, Expression 1 simplifies to: \[ 8k^3 - 6k - 4 \]
Expression 2:
\[ 9k^2 - 3k^3 + 4k - 39k^2 - 3k^3 + 4k - 3 \]
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Combine the \( k^3 \) terms: \[ -3k^3 - 3k^3 = -6k^3 \]
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Combine the \( k^2 \) terms: \[ 9k^2 - 39k^2 = -30k^2 \]
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Combine the \( k \) terms: \[ 4k + 4k = 8k \]
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Combine the constant terms: \[ -3 \]
So, Expression 2 simplifies to: \[ -6k^3 - 30k^2 + 8k - 3 \]
Final Step: Adding Expression 1 and Expression 2
Now, combine the two simplified expressions:
\[ (8k^3 - 6k - 4) + (-6k^3 - 30k^2 + 8k - 3) \]
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Combine the \( k^3 \) terms: \[ 8k^3 - 6k^3 = 2k^3 \]
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Combine the \( k^2 \) terms: \[ 0k^2 - 30k^2 = -30k^2 \]
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Combine the \( k \) terms: \[ -6k + 8k = 2k \]
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Combine the constants: \[ -4 - 3 = -7 \]
So, the final result, after combining both expressions, is: \[ \boxed{2k^3 - 30k^2 + 2k - 7} \]