#### Answer

$$4y^2(y - 3)(y + 3)$$

#### Work Step by Step

To factor this polynomial, we need to factor out the greatest common factor of both the coefficient and the variable:
The greatest common factor of the coefficients $4$ and $36$ is $4$.
The greatest common factor of the variables $y^4$ and $y^2$ is $y^2$.
Therefore, we will factor out $4y^2$ from each term to get:
$$4y^2(y^2 - 9)$$
We see that we now have a polynomial that is the difference of two squares, so we can further factor this polynomial. The formula for factoring the difference of two squares is given as:
$$A^2 - B^2 = (A + B)(A - B)$$
We now plug in the values for $A$, which is the $\sqrt y^2$ or $y$, and $B$, which is the $\sqrt 9$ or $3$, to get:
$$4y^2(y - 3)(y + 3)$$