Add $ \, \color{blue}{ 5a-7a^2+1 } \, $ and $ \, \color{orangered}{ 3a^2-2a+3 }$.

$$ \left( \color{blue}{5a-7a^2+1} \right) + \left( \color{orangered}{3a^2-2a+3} \right) = -4a^2+3a+4 $$

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

$$ \begin{aligned} P(x) &= -7a^2+5a+1 \\ Q(x) &= 3a^2-2a+3 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -7a^2 & 5a & 1 \\ \color{blue}{ + } & 3a^2 & -2a & 3 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -7a^2 & 5a & 1 \\ \color{blue}{ + } & 3a^2 & -2a & 3 \\ \hline & -4a^2 & 3a & 4 \end{array} $$

Polynomial Operations Calculator