Question
Multiply polynomial $ \, \color{blue}{ 9x^2+12x+4 } \, $ by $ \, \color{orangered}{ 2x+5 }$.
Answer
$$ \left( \color{blue}{9x^2+12x+4} \right) \cdot \left( \color{orangered}{2x+5} \right) = 18x^3+69x^2+68x+20 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{9x^2} & \color{blue}{12x} & \color{blue}{4} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{9x^2} & \color{blue}{12x} & \color{blue}{4} \\ \hline \color{blue}{2x} & \color{orangered}{18x^3} & \color{orangered}{24x^2} & \color{orangered}{8x} \\ \hline \color{blue}{5} & \color{orangered}{45x^2} & \color{orangered}{60x} & \color{orangered}{20} \\ \hline \end{darray} $$Combine like terms:
$$ 18x^3 + 24x^2 + 45x^2 + 8x + 60x + 20 = \\ 18x^3+69x^2+68x+20 $$This page was created using
Polynomial Operations Calculator