Add $ \, \color{blue}{ 4w+5-7w^2 } \, $ and $ \, \color{orangered}{ 3w^2-14 }$.

$$ \left( \color{blue}{4w+5-7w^2} \right) + \left( \color{orangered}{3w^2-14} \right) = -4w^2+4w-9 $$

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

$$ \begin{aligned} P(x) &= -7w^2+4w+5 \\ Q(x) &= 3w^2-14 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -7w^2 & 4w & 5 \\ \color{blue}{ + } & 3w^2 & & -14 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -7w^2 & 4w & 5 \\ \color{blue}{ + } & 3w^2 & & -14 \\ \hline & -4w^2 & 4w & -9 \end{array} $$

Polynomial Operations Calculator