Question
Add $ \, \color{blue}{ x+5x^2+7x^3 } \, $ and $ \, \color{orangered}{ 8x^3-x }$.
Answer
$$ \left( \color{blue}{x+5x^2+7x^3} \right) + \left( \color{orangered}{8x^3-x} \right) = 15x^3+5x^2 $$
Explanation
Step 1: First we have to write polynomials in descending order.
$$ \begin{aligned} P(x) &= 7x^3+5x^2+x \\ Q(x) &= 8x^3-x \\ \end{aligned} $$Step 2: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 7x^3 & 5x^2 & x \\ \color{blue}{ + } & 8x^3 & & -x \\ \hline \end{array} $$Step 3: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 7x^3 & 5x^2 & x \\ \color{blue}{ + } & 8x^3 & & -x \\ \hline & 15x^3 & 5x^2 & \end{array} $$This page was created using
Polynomial Operations Calculator