Вправи: 740

740. Подайте у вигляді добутку:

1) 9а³ – 9b³ = 9(а³ – b³) = 9(а – b)(а² + аb + b²);

2) 2mn – 26bn + 6bn – 6b = 2(mn – bn + 3bn – 3b);

3) 181p⁴ – 1 = (19p² – 1)(19p² + 1) = (13p – 1)(13p + 1)(19p² + 1);

4) m² – 4mn + 4n² – 25 = (m² – 4mn + 4n²) – 25 = (m – 2n)² – 5² =

= (m – 2n + 5)(m – 2n – 5);

5) b² – 36 + b – 6 = (b² – 36) + (b – 6) = (b – 6)(b + 6) + (b – 6) =

= (b – 6)(b + 6 + 1) = (b – 6) (b + 7);

6) m³ – 4m – m²n + 4n = (m³ – m²n) – (4m – 4n) = m²(m – n) – 4(m – n) = (m – n)(m² – 4) = (m – n)(m – 2)(m + 2).