To simplify the expression \( t^2 + 8t^2 - 5t + 9t^2 + 10t \), we can combine like terms.
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Combine the \( t^2 \) terms: \[ t^2 + 8t^2 + 9t^2 = (1 + 8 + 9)t^2 = 18t^2 \]
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Combine the \( t \) terms: \[ -5t + 10t = ( -5 + 10)t = 5t \]
Now we will put the combined results together: \[ 18t^2 + 5t \]
Thus, the simplified expression is: \[ \boxed{18t^2 + 5t} \]