Question
Multiply polynomial $ \, \color{blue}{ 3x^2+10x-8 } \, $ by $ \, \color{orangered}{ 3x-2 }$.
Answer
$$ \left( \color{blue}{3x^2+10x-8} \right) \cdot \left( \color{orangered}{3x-2} \right) = 9x^3+24x^2-44x+16 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{10x} & \color{blue}{-8} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{10x} & \color{blue}{-8} \\ \hline \color{blue}{3x} & \color{orangered}{9x^3} & \color{orangered}{30x^2} & \color{orangered}{-24x} \\ \hline \color{blue}{-2} & \color{orangered}{-6x^2} & \color{orangered}{-20x} & \color{orangered}{16} \\ \hline \end{darray} $$Combine like terms:
$$ 9x^3 + 30x^2-6x^2-24x-20x + 16 = \\ 9x^3+24x^2-44x+16 $$This page was created using
Polynomial Operations Calculator