Question
Multiply polynomial $ \, \color{blue}{ 4x-6 } \, $ by $ \, \color{orangered}{ 5x^2+4x+3 }$.
Answer
$$ \left( \color{blue}{4x-6} \right) \cdot \left( \color{orangered}{5x^2+4x+3} \right) = 20x^3-14x^2-12x-18 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{4x} & \color{blue}{3} \\ \hline \color{blue}{4x} & & & \\ \hline \color{blue}{-6} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{4x} & \color{blue}{3} \\ \hline \color{blue}{4x} & \color{orangered}{20x^3} & \color{orangered}{16x^2} & \color{orangered}{12x} \\ \hline \color{blue}{-6} & \color{orangered}{-30x^2} & \color{orangered}{-24x} & \color{orangered}{-18} \\ \hline \end{darray} $$Combine like terms:
$$ 20x^3 + 16x^2-30x^2 + 12x-24x-18 = \\ 20x^3-14x^2-12x-18 $$This page was created using
Polynomial Operations Calculator