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

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

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

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

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

$$ \begin{array}{lrrrrr} & & 4c^3 & -7c^2 & -3c & \\ \color{blue}{ + } & -4c^4 & & 2c^2 & & 4 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & & 4c^3 & -7c^2 & -3c & \\ \color{blue}{ + } & -4c^4 & & 2c^2 & & 4 \\ \hline & -4c^4 & 4c^3 & -5c^2 & -3c & 4 \end{array} $$

Polynomial Operations Calculator