Розділ 2. РОЗКЛАДАННЯ МНОГОЧЛЕНІВ » 625

Розклади на множники многочлен. a) ax4 – x4 + ax3 – x3 = x3(ax – x + a – 1) = x3(x(a – 1) + (a – 1) = x3(a – 1)(x + 1); б) x3 – x2y + x2 – xy = x(x2 – xy + x – y) = x(x(x – y) + (x – y)) = x(x – y)(x + 1); в) a2b – 6a2 – bc2 + 6c2 = (a2b – 6a2) – (bc2 – 6c2) = a2(b – 6) – c2(b – 6) = (b – 6)(a2 – c2) = (b – 6)(a – c)(a + c); г) ap2 – b + bp2 – a = (ap2 + bp2) – (a + b) = p2 • (a + b) – (a + b) = (a + b)(p2 – 1) = (a + b)(p – 1)(p + 1).