Question
Multiply polynomial $ \, \color{blue}{ 4x^2-6x+9 } \, $ by $ \, \color{orangered}{ 2x+3 }$.
Answer
$$ \left( \color{blue}{4x^2-6x+9} \right) \cdot \left( \color{orangered}{2x+3} \right) = 8x^3+27 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{-6x} & \color{blue}{9} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{-6x} & \color{blue}{9} \\ \hline \color{blue}{2x} & \color{orangered}{8x^3} & \color{orangered}{-12x^2} & \color{orangered}{18x} \\ \hline \color{blue}{3} & \color{orangered}{12x^2} & \color{orangered}{-18x} & \color{orangered}{27} \\ \hline \end{darray} $$Combine like terms:
$$ 8x^3-12x^2 + 12x^2 + 18x-18x + 27 = \\ 8x^3+27 $$This page was created using
Polynomial Operations Calculator