We are asked to simplify the expression $(x+4)^2 + (3x+2)(x-8)$.

1. Problem Description

We are asked to simplify the expression $(x+4)^2 + (3x+2)(x-8)$.

2. Solution Steps

First, we expand $(x+4)^2$:

$(x+4)^2 = (x+4)(x+4) = x^2 + 4x + 4x + 16 = x^2 + 8x + 16$

Next, we expand $(3x+2)(x-8)$:

$(3x+2)(x-8) = 3x^2 - 24x + 2x - 16 = 3x^2 - 22x - 16$

Now, we add the two expressions:

$(x^2 + 8x + 16) + (3x^2 - 22x - 16) = x^2 + 3x^2 + 8x - 22x + 16 - 16 = 4x^2 - 14x$

3. Final Answer

$4x^2 - 14x$