Let's simplify the expression step by step:
The expression is: \[ (16 - 12)^2 + 5(8 + 22) \cdot 53 - (1 + 4)^2 \]
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Simplify \( (16 - 12)^2 \): \[ 16 - 12 = 4 \implies (4)^2 = 16 \]
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Simplify \( (1 + 4)^2 \): \[ 1 + 4 = 5 \implies (5)^2 = 25 \]
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Simplify \( (8 + 22) \): \[ 8 + 22 = 30 \]
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Now, put this back into the expression: \[ 16 + 5 \cdot 30 \cdot 53 - 25 \]
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Now compute \( 5 \cdot 30 \): \[ 5 \cdot 30 = 150 \]
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Multiply \( 150 \cdot 53 \): \[ 150 \cdot 53 = 7950 \]
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Now substitute this back into the expression: \[ 16 + 7950 - 25 \]
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Combine the terms: \[ 16 - 25 = -9 \] \[ -9 + 7950 = 7941 \]
So the final simplified value of the numerator is \( 7941 \).
The provided options did not include this value. Please check the original expression and the options for any possible errors.