Вправи: 418

418. Розклади на множники вираз.

a) 6a(x – 2) + 8b(x – 2) + 4c(2 – x) = 6a(x – 2) + 8b(x – 2) – 4c(x – 2) = (x – 2)(6a + 8b – 4c);

б) (x³ + 1)(2x + 3) + 3(2x⁴ + 3x³) + (x³ – 1)(3 + 2x) = (x³ + 1)(2x + 3) + 3x³(2x + 3) + (x³ – 1)(2x + 3) = (2x + 3)(x³ + 1 + 3x³ + x³ – 1) = (2x + 3) • 5x³;

в) (x³ – 1) + 5a(x³ – 1) + b(1 – x³) = (x³ – 1) + 5a(x³ – 1) – b(x³ – 1) = (x³ – 1)(1 + 5a – b);

г) (2x – 1)(x² + 1) + (x² – 1)(2x – 1) + (1 – 2x)(x² + 2) = (2x – 1)(x² + 1) + (x² – 1)(2x – 1) – (2x – 1)(x² + 2) = (2x – 1)(x² + 1 + x² – 1 – x² – 2) = (2x – 1)(x² – 2).