Factorize the following polynomials.

(x² – 6x)² – 8(x² – 6x + 8) – 64

(x² – 6x) ² – 8(x² – 6x + 8) – 64

⟹ (x² – 6x) ² – 8(x² -6x) - 64 – 64

⟹ (x² – 6x) ² – 8(x² -6x) – 128

Put (x² -6x) = a

⟹ (a) ² – 8(a) – 128

⟹ a² – 8a – 128

⟹ a² – 16a + 8a - 128

⟹ a (a-16) + 8(a – 16)

⟹ (a + 8) × (a-16)

⟹ But a = (x² -6x)

⟹ ((x² -6x) + 8) × ((x² -6x) – 16)

⟹ (x² -6x + 8) × (x² -6x – 16)

⟹ (x² -4x – 2x + 8) × (x² -8x + 2x – 16)

⟹ (x(x-4) – 2(x-4)) × (x(x-8) + 2(x-8)

⟹ (x-2)(x-4)(x-8)(x+2)

Therefore, the factorized form = (x-2) (x-4) (x-8) (x+2)