Question
Multiply polynomial $ \, \color{blue}{ 7r-4 } \, $ by $ \, \color{orangered}{ 6r^2+6r+4 }$.
Answer
$$ \left( \color{blue}{7r-4} \right) \cdot \left( \color{orangered}{6r^2+6r+4} \right) = 42r^3+18r^2+4r-16 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6r^2} & \color{blue}{6r} & \color{blue}{4} \\ \hline \color{blue}{7r} & & & \\ \hline \color{blue}{-4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6r^2} & \color{blue}{6r} & \color{blue}{4} \\ \hline \color{blue}{7r} & \color{orangered}{42r^3} & \color{orangered}{42r^2} & \color{orangered}{28r} \\ \hline \color{blue}{-4} & \color{orangered}{-24r^2} & \color{orangered}{-24r} & \color{orangered}{-16} \\ \hline \end{darray} $$Combine like terms:
$$ 42r^3 + 42r^2-24r^2 + 28r-24r-16 = \\ 42r^3+18r^2+4r-16 $$This page was created using
Polynomial Operations Calculator