Is there easy way to factor polynomials for calculus? factor of $$4y^9-4y$$
comes out to be $$4y(y^4+1)(y^2+1)(y+1)(y-1)$$
How would you approach to factor?
PS: My math is very rusty.

\begin{align*}
4y^9-4y&=4y(y^8-1)\\
&=4y((y^4)^2-1)\\
&=4y(y^4-1)(y^4+1)\\
&=4y((y^2)^2-1)(y^4+1)\\
&=4y(y^2-1)(y^2+1)(y^4+1)\\
&=4y(y-1)(y+1)(y^2+1)(y^4+1).
\end{align*}
I am simply using $a^2-b^2=(a-b)(a+b)$. For example, at the second equation we took $a=y^4,\ b=1$.
