Add $ \, \color{blue}{ 4x^3-x^2 } \, $ and $ \, \color{orangered}{ 5x^2+x^3 }$.

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

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

$$ \begin{aligned} P(x) &= 4x^3-x^2 \\ Q(x) &= x^3+5x^2 \\ \end{aligned} $$

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

$$ \begin{array}{lrr} & 4x^3 & -x^2 \\ \color{blue}{ + } & x^3 & 5x^2 \\ \hline \end{array} $$

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

$$ \begin{array}{lrr} & 4x^3 & -x^2 \\ \color{blue}{ + } & x^3 & 5x^2 \\ \hline & 5x^3 & 4x^2 \end{array} $$

Polynomial Operations Calculator