To simplify the expression \( 5(3 + 4k) + 3(4 + k) \), we will distribute the constants in front of the parentheses.
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Distribute the \( 5 \) in \( 5(3 + 4k) \): \[ 5 \times 3 + 5 \times 4k = 15 + 20k \]
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Distribute the \( 3 \) in \( 3(4 + k) \): \[ 3 \times 4 + 3 \times k = 12 + 3k \]
Now, we combine the results from both distributions: \[ 15 + 20k + 12 + 3k \]
Next, we combine like terms:
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Combine the constant terms: \[ 15 + 12 = 27 \]
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Combine the \( k \) terms: \[ 20k + 3k = 23k \]
Putting it all together, the expression simplifies to: \[ 27 + 23k \]
Therefore, the expression equivalent to \( 5(3 + 4k) + 3(4 + k) \) is: \[ \boxed{27 + 23k} \]