How would I factor the following polynomial and show all of the work?
4y to the second power + 16y + 16

You have 4 different posts on factoring polynomials
1. You should have all posted in the same post
2. We are not suppose to help with homework.
If it is not homework please explain why you want help.

Apparently you want us to do your homework for you. I'll help, but you have to show that you're doing the work.

The general equation for a quadratic polynomial is

ax^2 + bx + c where a, b, and c are coefficients. In this case, x replaces your y. There's no difference in the problem; you just use y and not x.

Your equation is:

4y^2 + 16y + 16

Just like your last question the coefficient 4 (a in the general equation) and 16 (c in the general equation) are perfect squares. Perfect squares usually simplify factoring. Take their square roots and use them as possible coefficients in the factors.

Note that all coefficients are positive, so this will factor like this:

(ay+b)(cy+d)

where

ac = 4; \, bd = 16\, ad + bc = 16