To simplify the expression \((16−12)^2 + 5(8+22)53 − (1+4)^2\), we will break it down step by step:
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Calculate \(16 - 12\): \[ 16 - 12 = 4 \]
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Now square it: \[ (16 - 12)^2 = 4^2 = 16 \]
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Next, calculate \(8 + 22\): \[ 8 + 22 = 30 \]
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Now multiply by 5 and then by 53: \[ 5(30)53 = 5 \times 30 \times 53 = 150 \times 53 \] First, compute \(150 \times 53\): \[ 150 \times 53 = 7950 \]
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Next, calculate \(1 + 4\): \[ 1 + 4 = 5 \]
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Now square this result: \[ (1 + 4)^2 = 5^2 = 25 \]
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Now substitute everything back into the expression: \[ 16 + 7950 - 25 \]
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Now perform the addition and subtraction:
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Combine \(16 - 25\): \[ 16 - 25 = -9 \]
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Now add \(-9\) to \(7950\): \[ 7950 - 9 = 7941 \]
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Thus, the simplified numerator of the expression is \(\boxed{7941}\).
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