To find the value of the expression \( 4b^2 + b - 5 \) when \( b = 7 \), we can substitute 7 for \( b \) in the expression:
\[ 4(7)^2 + 7 - 5 \]
Now, calculate each part step-by-step:
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Calculate \( 7^2 \): \[ 7^2 = 49 \]
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Multiply by 4: \[ 4 \times 49 = 196 \]
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Now add 7 to this result: \[ 196 + 7 = 203 \]
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Finally, subtract 5: \[ 203 - 5 = 198 \]
Thus, the value of the expression \( 4b^2 + b - 5 \) when \( b = 7 \) is \( \boxed{198} \).