Question
Multiply polynomial $ \, \color{blue}{ 2x^2-8x-4 } \, $ by $ \, \color{orangered}{ 3x+2 }$.
Answer
$$ \left( \color{blue}{2x^2-8x-4} \right) \cdot \left( \color{orangered}{3x+2} \right) = 6x^3-20x^2-28x-8 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-8x} & \color{blue}{-4} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-8x} & \color{blue}{-4} \\ \hline \color{blue}{3x} & \color{orangered}{6x^3} & \color{orangered}{-24x^2} & \color{orangered}{-12x} \\ \hline \color{blue}{2} & \color{orangered}{4x^2} & \color{orangered}{-16x} & \color{orangered}{-8} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^3-24x^2 + 4x^2-12x-16x-8 = \\ 6x^3-20x^2-28x-8 $$This page was created using
Polynomial Operations Calculator