To simplify the expression \( 4 \left( (7 - 2)^2 \div 5 \right) \), follow these steps:
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Simplify inside the parentheses: \[ 7 - 2 = 5 \]
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Next, calculate \( (5)^2 \): \[ 5^2 = 25 \]
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Now, divide by 5: \[ 25 \div 5 = 5 \]
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Finally, multiply by 4: \[ 4 \times 5 = 20 \]
Thus, the fully simplified expression is: \[ \boxed{20} \]