Вправи: 631

631. Розклади на множники многочлен.

a) ac² + bc – bc² – ac = c(ac + b – bc – a) = c(ac – bc – (a – b)) = c(c(a – b) – (a – b)) = c(a – b)(c – 1);

б) a²b + 3a + 3ab + a² = a(ab + 3 + 3b + a) = a(ab + a + 3b + 3) = a(a(b + 1) + 3(b + 1)) = a(b + 1)(a + 3);

в) ax – a² + ax² – a³ = a(x – a + x² – a²) = a(x – a + (x – a)(x + a)) = a(x – a)(1 + x + a)

г) 9a² + 6ab + b² + 3a + b = (3a + b)² + (3a + b) = (3a + b)(3a + b + 1);