Question
Multiply polynomial $ \, \color{blue}{ 7a+2 } \, $ by $ \, \color{orangered}{ 2a^2-5a+3 }$.
Answer
$$ \left( \color{blue}{7a+2} \right) \cdot \left( \color{orangered}{2a^2-5a+3} \right) = 14a^3-31a^2+11a+6 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2a^2} & \color{blue}{-5a} & \color{blue}{3} \\ \hline \color{blue}{7a} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2a^2} & \color{blue}{-5a} & \color{blue}{3} \\ \hline \color{blue}{7a} & \color{orangered}{14a^3} & \color{orangered}{-35a^2} & \color{orangered}{21a} \\ \hline \color{blue}{2} & \color{orangered}{4a^2} & \color{orangered}{-10a} & \color{orangered}{6} \\ \hline \end{darray} $$Combine like terms:
$$ 14a^3-35a^2 + 4a^2 + 21a-10a + 6 = \\ 14a^3-31a^2+11a+6 $$This page was created using
Polynomial Operations Calculator