Answer
$$y(y - 2)(y + 2)(y^2 + 4)$$
Work Step by Step
Looking at this binomial, we see that we can first factor out a $y$ from each of the terms:
$$y(y^4 - 16)$$
We see that the binomial within the parentheses can be factored as the product of two squares according to the following formula:
$$A^2 - B^2 = (A - B)(A + B)$$
where $A$ is the square root of the first term and $B$ is the square root of the second term.
In this case, $A$ is the $\sqrt(y^4)$, or $y^2$ and $B$ is the $\sqrt(16)$ or $4$. Let us plug these values into the formula:
$$y(y^2 - 4)(y^2 + 4)$$
We can factor the $y^2 - 4$ term even further because it is also a difference of two squares. Here, the $A$ term is $\sqrt y^2$ or $y$ and $B$ is the $\sqrt 4$ or $2$. We use these values to plug into the equation for the difference of two squares:
$$y(y - 2)(y + 2)(y^2 + 4)$$