To solve the expression \( 6 - 4(3 - 1)^2 + 16 \), we follow the order of operations (PEMDAS/BODMAS):
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Parentheses/Brackets: Solve inside the parentheses first. \[ 3 - 1 = 2 \]
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Exponents: Next, we square the result. \[ (2)^2 = 4 \]
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Multiplication: Now substitute back into the expression and perform the multiplication. \[ 6 - 4(4) + 16 \] \[ 4 \cdot 4 = 16 \]
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Rewrite the expression: \[ 6 - 16 + 16 \]
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Addition/Subtraction from left to right:
- First, perform \( 6 - 16 \): \[ 6 - 16 = -10 \]
- Then add 16: \[ -10 + 16 = 6 \]
Finally, the result of the expression \( 6 - 4(3 - 1)^2 + 16 \) is \(\boxed{6}\).
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