Subtract polynomials: $ \, \color{blue}{ -7r-4r^3-7r^2 } \, $ , $ \, \color{orangered}{ 4r+7r^3-2r^2 }$.

$$ \left( \color{blue}{-7r-4r^3-7r^2} \right) - \left( \color{orangered}{4r+7r^3-2r^2} \right) = -11r^3-5r^2-11r $$

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

$$ \begin{aligned} P(x) &= -4r^3-7r^2-7r \\ Q(x) &= 7r^3-2r^2+4r \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -4r^3 & -7r^2 & -7r \\ \color{red}{ - } & 7r^3 & -2r^2 & 4r \\ \hline \end{array} $$

Step 3: Change ALL the signs in the second row.

$$ \begin{array}{lrrr} & -4r^3 & -7r^2 & -7r \\ \color{red}{ - } & -7r^3 & 2r^2 & -4r \\ \hline \end{array} $$

Step 4: Combine like terms (add each column):

$$ \begin{array}{lrrr} & -4r^3 & -7r^2 & -7r \\ \color{red}{ - } & -7r^3 & 2r^2 & -4r \\ \hline & 3r^3 & -9r^2 & -3r \end{array} $$

Polynomial Operations Calculator