Add $ \, \color{blue}{ t^2+3t^3-3 } \, $ and $ \, \color{orangered}{ 2t^2+7t-2t^3 }$.

$$ \left( \color{blue}{t^2+3t^3-3} \right) + \left( \color{orangered}{2t^2+7t-2t^3} \right) = t^3+3t^2+7t-3 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 3t^3+t^2-3 \\ Q(x) &= -2t^3+2t^2+7t \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrrrr} & 3t^3 & t^2 & & -3 \\ \color{blue}{ + } & -2t^3 & 2t^2 & 7t & \\ \hline \end{array} $$

Step 3: Combine like terms (add each column):

$$ \begin{array}{lrrrr} & 3t^3 & t^2 & & -3 \\ \color{blue}{ + } & -2t^3 & 2t^2 & 7t & \\ \hline & t^3 & 3t^2 & 7t & -3 \end{array} $$

Polynomial Operations Calculator