Вправи: 442

442. Розклади на множники многочлен.

a) 3m² + 9mn – 2m – 6n = (3m² + 9mn) – (2m + 6n) = 3m(m + 3n) – 2(m + 3n) = (m + 3n)(3m – 2;

б) a³ – a²n – 3a + 3n = (a³ – a²n) – (3a – 3n) = a²(a – n) – 3(a – n) = (a – n)(a² – 3);

в) y³ – 3y⁵ + 3y² – 9y⁴ = (y³ + 3y²) – (3y⁵ + 9y⁴) = y²(y + 3) – 3y⁴(y + 3) = (y + 3)(y² – 3y⁴)

г) 3a³ + 12a² – a – 4 = 3a³ + 12a² – (a + 4) = 3a²(a + 4) – (a + 4) = (a + 4)(3a² – 1);

ґ) 4x²y² – 4xy – 5axy + 5a = (4x²y² – 4xy) – (5axy – 5a) = 4xy(xy – 1) – 5a(xy – 1) = (xy – 1)(4xy – 1);

д) a³x² + a²x³ – a – x = (a³x² + a²x³) – (a + x) = a²x²(a + x) – (a + x) = (a + x)(a²x² – 1).