Question
Multiply polynomial $ \, \color{blue}{ 9x^2-6x+1 } \, $ by $ \, \color{orangered}{ 3x-1 }$.
Answer
$$ \left( \color{blue}{9x^2-6x+1} \right) \cdot \left( \color{orangered}{3x-1} \right) = 27x^3-27x^2+9x-1 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{9x^2} & \color{blue}{-6x} & \color{blue}{1} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{9x^2} & \color{blue}{-6x} & \color{blue}{1} \\ \hline \color{blue}{3x} & \color{orangered}{27x^3} & \color{orangered}{-18x^2} & \color{orangered}{3x} \\ \hline \color{blue}{-1} & \color{orangered}{-9x^2} & \color{orangered}{6x} & \color{orangered}{-1} \\ \hline \end{darray} $$Combine like terms:
$$ 27x^3-18x^2-9x^2 + 3x + 6x-1 = \\ 27x^3-27x^2+9x-1 $$This page was created using
Polynomial Operations Calculator