Question
Multiply polynomial $ \, \color{blue}{ 4x-3 } \, $ by $ \, \color{orangered}{ 3x^2-3x+3 }$.
Answer
$$ \left( \color{blue}{4x-3} \right) \cdot \left( \color{orangered}{3x^2-3x+3} \right) = 12x^3-21x^2+21x-9 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-3x} & \color{blue}{3} \\ \hline \color{blue}{4x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-3x} & \color{blue}{3} \\ \hline \color{blue}{4x} & \color{orangered}{12x^3} & \color{orangered}{-12x^2} & \color{orangered}{12x} \\ \hline \color{blue}{-3} & \color{orangered}{-9x^2} & \color{orangered}{9x} & \color{orangered}{-9} \\ \hline \end{darray} $$Combine like terms:
$$ 12x^3-12x^2-9x^2 + 12x + 9x-9 = \\ 12x^3-21x^2+21x-9 $$This page was created using
Polynomial Operations Calculator