Simplify:

Answer:

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