Question
Multiply polynomial $ \, \color{blue}{ 7v+5 } \, $ by $ \, \color{orangered}{ 8v^2+5v-6 }$.
Answer
$$ \left( \color{blue}{7v+5} \right) \cdot \left( \color{orangered}{8v^2+5v-6} \right) = 56v^3+75v^2-17v-30 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8v^2} & \color{blue}{5v} & \color{blue}{-6} \\ \hline \color{blue}{7v} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8v^2} & \color{blue}{5v} & \color{blue}{-6} \\ \hline \color{blue}{7v} & \color{orangered}{56v^3} & \color{orangered}{35v^2} & \color{orangered}{-42v} \\ \hline \color{blue}{5} & \color{orangered}{40v^2} & \color{orangered}{25v} & \color{orangered}{-30} \\ \hline \end{darray} $$Combine like terms:
$$ 56v^3 + 35v^2 + 40v^2-42v + 25v-30 = \\ 56v^3+75v^2-17v-30 $$This page was created using
Polynomial Operations Calculator