Question
Multiply polynomial $ \, \color{blue}{ 2x-4 } \, $ by $ \, \color{orangered}{ 3x^2-3x+4 }$.
Answer
$$ \left( \color{blue}{2x-4} \right) \cdot \left( \color{orangered}{3x^2-3x+4} \right) = 6x^3-18x^2+20x-16 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-3x} & \color{blue}{4} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-3x} & \color{blue}{4} \\ \hline \color{blue}{2x} & \color{orangered}{6x^3} & \color{orangered}{-6x^2} & \color{orangered}{8x} \\ \hline \color{blue}{-4} & \color{orangered}{-12x^2} & \color{orangered}{12x} & \color{orangered}{-16} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^3-6x^2-12x^2 + 8x + 12x-16 = \\ 6x^3-18x^2+20x-16 $$This page was created using
Polynomial Operations Calculator