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