Question
Multiply polynomial $ \, \color{blue}{ a+5 } \, $ by $ \, \color{orangered}{ 7a^2-a+5 }$.
Answer
$$ \left( \color{blue}{a+5} \right) \cdot \left( \color{orangered}{7a^2-a+5} \right) = 7a^3+34a^2+25 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{7a^2} & \color{blue}{-a} & \color{blue}{5} \\ \hline \color{blue}{a} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{7a^2} & \color{blue}{-a} & \color{blue}{5} \\ \hline \color{blue}{a} & \color{orangered}{7a^3} & \color{orangered}{-a^2} & \color{orangered}{5a} \\ \hline \color{blue}{5} & \color{orangered}{35a^2} & \color{orangered}{-5a} & \color{orangered}{25} \\ \hline \end{darray} $$Combine like terms:
$$ 7a^3-a^2 + 35a^2 + 5a-5a + 25 = \\ 7a^3+34a^2+25 $$This page was created using
Polynomial Operations Calculator