To evaluate the expression \( 7 \cdot (6 + 2)^2 - 3^2 \), we'll follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).
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Calculate inside the parentheses: \[ 6 + 2 = 8 \]
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Now replace \( (6 + 2) \) with \( 8 \) and evaluate the exponent: \[ (8)^2 = 64 \]
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Now substitute back into the expression: \[ 7 \cdot 64 - 3^2 \]
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Calculate \( 3^2 \): \[ 3^2 = 9 \]
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Now replace \( 3^2 \) with \( 9 \): \[ 7 \cdot 64 - 9 \]
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Now perform the multiplication: \[ 7 \cdot 64 = 448 \]
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Finally, subtract \( 9 \): \[ 448 - 9 = 439 \]
Thus, the value of the expression \( 7 \cdot (6 + 2)^2 - 3^2 \) is \( 439 \).
The answer is B. 439.