Find $ \left(9t+1\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ 9t } $ and $ B = \color{red}{ 1 }$.

$$ \begin{aligned}\left(9t+1\right)^2 = \color{blue}{\left( 9t \right)^2} +2 \cdot 9t \cdot 1 + \color{red}{1^2} = 81t^2+18t+1\end{aligned} $$

Find $ \left(3t+1\right)^3 $ using formula

$$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$

where $ A = 3t $ and $ B = 1 $.

$$ \left(3t+1\right)^3 = \left( 3t \right)^3+3 \cdot \left( 3t \right)^2 \cdot 1 + 3 \cdot 3t \cdot 1^2+1^3 = 27t^3+27t^2+9t+1 $$

Combine like terms:

$$ 108t^3+81t^2+18t+1 = 108t^3+81t^2+18t+1 $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( 324t^4+351t^3+135t^2+21t+1 \right) = -324t^4-351t^3-135t^2-21t-1 $$

Combine like terms:

$$ \color{blue}{108t^3} + \color{red}{81t^2} + \color{green}{18t} + \, \color{orange}{ \cancel{1}} \,-324t^4 \color{blue}{-351t^3} \color{red}{-135t^2} \color{green}{-21t} \, \color{orange}{ -\cancel{1}} \, = \\ = -324t^4 \color{blue}{-243t^3} \color{red}{-54t^2} \color{green}{-3t} $$