Simplify:

(i)

(x² – y²) (x² + y²) (x⁴ + y⁴)

= [(x²)² – (y²)²] (x⁴ + y⁴)

= (x⁴ – y⁴) (x⁴ – y⁴)

= [(x⁴)² – (y⁴)²]

= x⁸ – y⁸

(ii)

[(2x)² – (1)²] (4x² + 1) (16x⁴ + 1)

= (4x² – 1) (4x² + 1) (16x⁴ + 1) 1

= [(4x²)² – (1)²] (16x⁴ + 1) 1

= (16x⁴ – 1) (16x⁴ + 1) 1

= [(16x⁴)² – (1)²] 1

= 256x⁸ – 1

(iii)

(7m)² + (8n)² – 112mn + (7m)² + (8n)² + 112mn

= 49m² + 64n² + 49m² + 64n²

= 98m² + 64n² + 64n²

= 98m² + 128n²

(iv)

(2.5p)² + (1.5q)² – 2 (2.5p) (1.5q) – (1.5p)² – (2.5q)² + 2 (1.5p) (2.5q)

= 6.25p² + 2.25q² – 2.25p² – 6.25q²

= 4p² – 6.25q² + 2.25q²

= 4p² – 4q²

= 4 (p² – q²)

(v)

_(m²)² – 2 (m²) (n²) (m) + (n²m)² + 2m³n²

_{= m}⁴ – 2m³n² + (n²m)² + 2m³n²

_{= m}⁴ + n⁴m² – 2m³n² + 2m³n²

_{= m}⁴ + m²n⁴

_{= m}² (m² + n⁴)