Add $ \, \color{blue}{ 7a-6a^3+a^2 } \, $ and $ \, \color{orangered}{ 2-3a^2+a }$.

$$ \left( \color{blue}{7a-6a^3+a^2} \right) + \left( \color{orangered}{2-3a^2+a} \right) = -6a^3-2a^2+8a+2 $$

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

$$ \begin{aligned} P(x) &= -6a^3+a^2+7a \\ Q(x) &= -3a^2+a+2 \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & -6a^3 & a^2 & 7a & \\ \color{blue}{ + } & & -3a^2 & a & 2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & -6a^3 & a^2 & 7a & \\ \color{blue}{ + } & & -3a^2 & a & 2 \\ \hline & -6a^3 & -2a^2 & 8a & 2 \end{array} $$

Polynomial Operations Calculator