Expanding the left side:
(4x-8)²( x-8) = (4x-8)(4x-8)(x-8)
= (16x² - 32x - 32x + 64)(x-8)
= (16x² - 64x + 64)(x-8)
= 16x³ - 64x² + 64x - 128x² + 512 - 512
= 16x³ - 192x² + 64x - 512

Expanding the right side:
(4x-8)(x-8)² = (4x-8)(x-8)(x-8)
= (4x-8)(x² - 16x + 64)
= 4x³ - 64x² + 256x - 8x² + 128x - 512
= 4x³ - 72x² + 384x - 512

Therefore, (4x-8)²( x-8) is NOT equal to (4x-8)(x-8)².