Add $ \, \color{blue}{ x^5+x^3 } \, $ and $ \, \color{orangered}{ 6x-x^3+6x^5 }$.

$$ \left( \color{blue}{x^5+x^3} \right) + \left( \color{orangered}{6x-x^3+6x^5} \right) = 7x^5+6x $$

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

$$ \begin{aligned} P(x) &= x^5+x^3 \\ Q(x) &= 6x^5-x^3+6x \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & x^5 & x^3 & \\ \color{blue}{ + } & 6x^5 & -x^3 & 6x \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & x^5 & x^3 & \\ \color{blue}{ + } & 6x^5 & -x^3 & 6x \\ \hline & 7x^5 & & 6x \end{array} $$

Polynomial Operations Calculator