Question
Multiply polynomial $ \, \color{blue}{ x+10 } \, $ by $ \, \color{orangered}{ 3x^2-3x+2 }$.
Answer
$$ \left( \color{blue}{x+10} \right) \cdot \left( \color{orangered}{3x^2-3x+2} \right) = 3x^3+27x^2-28x+20 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-3x} & \color{blue}{2} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{10} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-3x} & \color{blue}{2} \\ \hline \color{blue}{x} & \color{orangered}{3x^3} & \color{orangered}{-3x^2} & \color{orangered}{2x} \\ \hline \color{blue}{10} & \color{orangered}{30x^2} & \color{orangered}{-30x} & \color{orangered}{20} \\ \hline \end{darray} $$Combine like terms:
$$ 3x^3-3x^2 + 30x^2 + 2x-30x + 20 = \\ 3x^3+27x^2-28x+20 $$This page was created using
Polynomial Operations Calculator