Add $ \, \color{blue}{ -4x+4x^3+7 } \, $ and $ \, \color{orangered}{ 3x^2-9-3x }$.

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

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

$$ \begin{aligned} P(x) &= 4x^3-4x+7 \\ Q(x) &= 3x^2-3x-9 \\ \end{aligned} $$

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

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

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

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

Polynomial Operations Calculator