(y+16)(y-4)(y+4)

To simplify the expression \((y + 16)(y - 4)(y + 4)\), we can first recognize that \((y - 4)(y + 4)\) is a difference of squares:

\[ (y - 4)(y + 4) = y^2 - 16 \]

Now, we can rewrite the original expression as:

\[ (y + 16)(y^2 - 16) \]

Next, we can apply the distributive property (also known as the FOIL method for binomials) to expand this:

\[ (y + 16)(y^2 - 16) = y(y^2 - 16) + 16(y^2 - 16) \]

Calculating each part:

1. \(y(y^2 - 16) = y^3 - 16y\)
2. \(16(y^2 - 16) = 16y^2 - 256\)

Now, combine the two results:

\[ y^3 - 16y + 16y^2 - 256 \]

To write it in standard form, we reorganize it by degrees:

\[ y^3 + 16y^2 - 16y - 256 \]

Thus, the simplified form of the expression \((y + 16)(y - 4)(y + 4)\) is:

\[ \boxed{y^3 + 16y^2 - 16y - 256} \]