Add.

Question

(t^3+9t^2+6t+1)+(5t^3+4t^2+4t+7)

Answer 1

To add the polynomials \( (t^3 + 9t^2 + 6t + 1) \) and \( (5t^3 + 4t^2 + 4t + 7) \), we combine like terms.

1. Combine the \( t^3 \) terms: \[ t^3 + 5t^3 = 6t^3 \]

2. Combine the \( t^2 \) terms: \[ 9t^2 + 4t^2 = 13t^2 \]

3. Combine the \( t \) terms: \[ 6t + 4t = 10t \]

4. Combine the constant terms: \[ 1 + 7 = 8 \]

Now, putting it all together, we have: \[ 6t^3 + 13t^2 + 10t + 8 \]

Thus, the sum of the two polynomials is: \[ \boxed{6t^3 + 13t^2 + 10t + 8} \]