Question
Multiply polynomial $ \, \color{blue}{ 3x^2+2x-3 } \, $ by $ \, \color{orangered}{ 4x^2-5 }$.
Answer
$$ \left( \color{blue}{3x^2+2x-3} \right) \cdot \left( \color{orangered}{4x^2-5} \right) = 12x^4+8x^3-27x^2-10x+15 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{2x} & \color{blue}{-3} \\ \hline \color{blue}{4x^2} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{2x} & \color{blue}{-3} \\ \hline \color{blue}{4x^2} & \color{orangered}{12x^4} & \color{orangered}{8x^3} & \color{orangered}{-12x^2} \\ \hline \color{blue}{-5} & \color{orangered}{-15x^2} & \color{orangered}{-10x} & \color{orangered}{15} \\ \hline \end{darray} $$Combine like terms:
$$ 12x^4 + 8x^3-15x^2-12x^2-10x + 15 = \\ 12x^4+8x^3-27x^2-10x+15 $$This page was created using
Polynomial Operations Calculator