Let's simplify the expression step by step:
The expression given is:
\[ (16 - 12)^2 + 5(8 + 22) \cdot 53 - (1 + 4)^2 \]
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Calculate \( (16 - 12)^2 \): \[ 16 - 12 = 4 \implies (16 - 12)^2 = 4^2 = 16 \]
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Calculate \( (8 + 22) \): \[ 8 + 22 = 30 \]
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Now multiply by 5 and 53: \[ 5(8 + 22) \cdot 53 = 5 \cdot 30 \cdot 53 \]
First, calculate \( 5 \cdot 30 \): \[ 5 \cdot 30 = 150 \]
Now, multiply by 53: \[ 150 \cdot 53 = 7950 \]
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Calculate \( (1 + 4)^2 \): \[ 1 + 4 = 5 \implies (1 + 4)^2 = 5^2 = 25 \]
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Combine everything: \[ (16 - 12)^2 + 5(8 + 22) \cdot 53 - (1 + 4)^2 = 16 + 7950 - 25 \]
Combine these: \[ 16 + 7950 - 25 = 16 - 25 + 7950 = -9 + 7950 = 7941 \]
Thus, the simplified numerator is: \[ \boxed{7941} \]
None of the answer options listed (54, 100, 76, 42+60) match, indicating either an error in the choices or the initial expression provided. If the expression or choices were misunderstood, please clarify to ensure a correct response.
1 answer