How to multiply polynominals I can't figure out how to multiply these polynominals $$(5x^2+3x^4-7x^3+5x+8)(2x^2-4x+9-6x^2+7x)$$
I tried multiplying like this
$$(5x^2+3x^4-7x^3+5x+8)(2x^2-4x+9-6x^2+7x)$$
$$3x^4-7x^3+(5x^2)(2x^2)(-6x^2)+(5x)(7x)(-4x)+(8)(9)$$
$$3x^4-7x^3-60x^2-140x+72$$
It says the answer is $$-12x^6-19x^5-14x^4-68x^3+28x^2+69x+72$$ but how did they get it?

To multiply two polynomials, distribute each term in the left set of parentheses over the entire collection of terms in the right set of parentheses. Your example would start out like:
$$
\begin{align*}
& (\color{red}{5x^2+3x^4-7x^3+5x+8})(2x^2-4x+9-6x^2+7x)\\
= & \color{red}{5x^2}(2x^2-4x+9-6x^2+7x)\\
& \color{red}{+ 3x^4}(2x^2-4x+9-6x^2+7x)\\
& \color{red}{- 7x^3}(2x^2-4x+9-6x^2+7x)\\
& \color{red}{+ 5x}(2x^2-4x+9-6x^2+7x)\\
& \color{red}{+ 8}(2x^2-4x+9-6x^2+7x).
\end{align*}
$$
Can you take it from here?
