Question
Multiply polynomial $ \, \color{blue}{ 3x-2 } \, $ by $ \, \color{orangered}{ 2x^2+3x-1 }$.
Answer
$$ \left( \color{blue}{3x-2} \right) \cdot \left( \color{orangered}{2x^2+3x-1} \right) = 6x^3+5x^2-9x+2 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{3x} & \color{blue}{-1} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{3x} & \color{blue}{-1} \\ \hline \color{blue}{3x} & \color{orangered}{6x^3} & \color{orangered}{9x^2} & \color{orangered}{-3x} \\ \hline \color{blue}{-2} & \color{orangered}{-4x^2} & \color{orangered}{-6x} & \color{orangered}{2} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^3 + 9x^2-4x^2-3x-6x + 2 = \\ 6x^3+5x^2-9x+2 $$This page was created using
Polynomial Operations Calculator