8) F

Break the problem into smaller parts

__1st step: __

x² (1 – 16x²) = x² – 16x⁴

__2nd step: __

2x³ (4x – 1) = 8x⁴ – 2x³

__3rd step: __

__ x² – 16x⁴
__8x⁴ – 2x³

__4th step: __

4 – __ x² – 16x⁴
__ 8x⁴ – 2x³

__4 (8x⁴ – 2x³) – (x² – 16x⁴)
__ 8x⁴ – 2x³

__32x⁴ – 8x³ – x² + 16x⁴
__ 8x⁴ – 2x³

__48x⁴ – 8x³ – x²
__ 8x⁴ – 2x³

__x² (48x² – 8x – 1)
__ x² (8x² – 2x)

__48x² – 8x – 1
__ 8x² – 2x

__5th step: Factorising the numerator__

**
**48x² – 8x – 1

48x² – 12x + 4x – 1

12x (4x – 1) + 1 (4x – 1)

(12x + 1) (4x – 1)

__6th step: Factorising the denominator__

8x² – 2x

2x (4x – 1)

__7th step: __

__(12x + 1) (4x – 1)
__ 2x (4x – 1)

__(12x + 1)
__ 2x

__12x__ + __ 1
__ 2x 2x

6 + __ 1
__ 2x