Let's solve the expression step-by-step:
Given expression: \[ 6 - 4(3 - 1)^2 + 16 \]
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Calculate the expression inside the parentheses: \[ 3 - 1 = 2 \]
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Now substitute that back into the expression: \[ 6 - 4(2)^2 + 16 \]
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Square the result: \[ 2^2 = 4 \]
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Now substitute that into the expression: \[ 6 - 4(4) + 16 \]
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Multiply: \[ 4(4) = 16 \]
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Now substitute that back: \[ 6 - 16 + 16 \]
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Perform the addition and subtraction from left to right: \[ 6 - 16 = -10 \] \[ -10 + 16 = 6 \]
So, the final answer is: \[ \boxed{6} \]