Let's simplify the expression step by step.
The expression is:
\[ (16 - 12)^2 + 5(8 + 22)53 - (1 + 4)^2 \]
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Calculate \( (16 - 12)^2 \): \[ (16 - 12) = 4 \quad \text{so} \quad (16 - 12)^2 = 4^2 = 16 \]
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Calculate \( 8 + 22 \): \[ 8 + 22 = 30 \]
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Multiply by \( 5 \) and \( 53 \): \[ 5(8 + 22)53 = 5 \times 30 \times 53 \] First calculate \( 5 \times 30 \): \[ 5 \times 30 = 150 \]
Now multiply \( 150 \times 53 \): \[ 150 \times 53 = 7950 \]
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Calculate \( (1 + 4)^2 \): \[ (1 + 4) = 5 \quad \text{so} \quad (1 + 4)^2 = 5^2 = 25 \]
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Combine these results: Now we can add and subtract these numbers: \[ 16 + 7950 - 25 \]
First, combine \( 16 - 25 \): \[ 16 - 25 = -9 \]
Now add \( 7950 \): \[ -9 + 7950 = 7941 \]
Therefore, the simplified result of the entire expression is 7941. None of the provided responses correspond with this result. However, I can conclude that based on the calculations made, the numerator after simplification is 7941.