To simplify the expression \( 25(34p + 56w) + 15(12p - 623w) \), follow these steps:
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Distribute \( 25 \) in the first part: \[ 25 \cdot 34p + 25 \cdot 56w = 850p + 1400w \]
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Distribute \( 15 \) in the second part: \[ 15 \cdot 12p + 15 \cdot (-623w) = 180p - 9345w \]
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Combine both results: \[ 850p + 1400w + 180p - 9345w \]
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Combine like terms:
- For \( p \): \[ 850p + 180p = 1030p \]
- For \( w \): \[ 1400w - 9345w = -7945w \]
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The final simplified expression is: \[ 1030p - 7945w \]
Final Answer: \[ 1030p - 7945w \]