Question
Multiply polynomial $ \, \color{blue}{ 6x+2 } \, $ by $ \, \color{orangered}{ 2x^2-6x+1 }$.
Answer
$$ \left( \color{blue}{6x+2} \right) \cdot \left( \color{orangered}{2x^2-6x+1} \right) = 12x^3-32x^2-6x+2 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-6x} & \color{blue}{1} \\ \hline \color{blue}{6x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-6x} & \color{blue}{1} \\ \hline \color{blue}{6x} & \color{orangered}{12x^3} & \color{orangered}{-36x^2} & \color{orangered}{6x} \\ \hline \color{blue}{2} & \color{orangered}{4x^2} & \color{orangered}{-12x} & \color{orangered}{2} \\ \hline \end{darray} $$Combine like terms:
$$ 12x^3-36x^2 + 4x^2 + 6x-12x + 2 = \\ 12x^3-32x^2-6x+2 $$This page was created using
Polynomial Operations Calculator