Add $ \, \color{blue}{ -4x+4x^3+7 } \, $ and $ \, \color{orangered}{ -3x^3-9+3x }$.

$$ \left( \color{blue}{-4x+4x^3+7} \right) + \left( \color{orangered}{-3x^3-9+3x} \right) = x^3-x-2 $$

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

$$ \begin{aligned} P(x) &= 4x^3-4x+7 \\ Q(x) &= -3x^3+3x-9 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 4x^3 & -4x & 7 \\ \color{blue}{ + } & -3x^3 & 3x & -9 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 4x^3 & -4x & 7 \\ \color{blue}{ + } & -3x^3 & 3x & -9 \\ \hline & x^3 & -x & -2 \end{array} $$

Polynomial Operations Calculator