Вправи: 816

816. Розкладіть на множники:

1) 127 + b³ = (13)³ + b³ = (13 + b)(19 – 13b + b²);

2) 18x³ – 8 = (12x)³ – 2³ = (12x – 2)(14x² + 12x ∙ 2 + 4) = (12x – 2)(14x² + x + 4);

3) 1 + 125p³ = 1³ + (5р)³ = (1 + 5p)(1 – 5p + 25р²);

4) 0,064m³ – 11000n³ =(0,4m)³ – (0,1n)³ = (0,4m – 0,1n)((0,4m)² + 0,4m ∙ 0,1n + (0,1n)²) = (0,4m – 0,1n)(0,16m² + 0,04mn + 0,01n²);

5) 278a³ + 827b³ = (32a)³ + (23b)³ = (32a + 23b)((32a)² – 32a ∙ 23b + (23b)²) = (32a + 23b)(94a² – ab + 49b²);

6) 216p³ – 1216q³ = (6p)³ – (16q)³ = (6p – 16q)(6p)² + 6p ∙ 16q + (16q)² = (6p – 16q)(36p² + pq + 136q²).