The volume of a square prism is 144x3 + 216 x2 + 81x. what is an expression that could describe the perimeter of one of the prism ’ s square faces? plz include steps of how it was done. you

The answer is 16x + 12.

The volume of a prism is:
V = l * w * h
l - length, w - width, h - height

144x³ + 216x² + 81x = l * w * h
9x * 16x² + 9x * 24x + 9x * 9 = l * w * h
9x(16x² + 24x + 9) = l * w * h
9x((4x)² + 2 * 4x * 3 + 3²) = l * w * h
9x(4x + 3)² = l * w * h
9x(4x + 3)(4x + 3) = l * w * h

So, one side is 9x, other is 4x + 3 and another is 4x + 3.
Square face will have both sides the same, so its sides are 4x + 3. Perimeter of a square is 4 times its side:
P = 4 * (4x + 3) = 4 * 4x + 4 * 3 = 16x + 12