Question
Multiply polynomial $ \, \color{blue}{ q-2 } \, $ by $ \, \color{orangered}{ 4q^2+3q+1 }$.
Answer
$$ \left( \color{blue}{q-2} \right) \cdot \left( \color{orangered}{4q^2+3q+1} \right) = 4q^3-5q^2-5q-2 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4q^2} & \color{blue}{3q} & \color{blue}{1} \\ \hline \color{blue}{q} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4q^2} & \color{blue}{3q} & \color{blue}{1} \\ \hline \color{blue}{q} & \color{orangered}{4q^3} & \color{orangered}{3q^2} & \color{orangered}{q} \\ \hline \color{blue}{-2} & \color{orangered}{-8q^2} & \color{orangered}{-6q} & \color{orangered}{-2} \\ \hline \end{darray} $$Combine like terms:
$$ 4q^3 + 3q^2-8q^2 + q-6q-2 = \\ 4q^3-5q^2-5q-2 $$This page was created using
Polynomial Operations Calculator