Add $ \, \color{blue}{ 2x^4+x } \, $ and $ \, \color{orangered}{ 7x-2x^2 }$.

$$ \left( \color{blue}{2x^4+x} \right) + \left( \color{orangered}{7x-2x^2} \right) = 2x^4-2x^2+8x $$

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

$$ \begin{aligned} P(x) &= 2x^4+x \\ Q(x) &= -2x^2+7x \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 2x^4 & & x \\ \color{blue}{ + } & & -2x^2 & 7x \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 2x^4 & & x \\ \color{blue}{ + } & & -2x^2 & 7x \\ \hline & 2x^4 & -2x^2 & 8x \end{array} $$

Polynomial Operations Calculator