Розділ 2. РОЗКЛАДАННЯ МНОГОЧЛЕНІВ » 630

Розклади на множники многочлен. a) a2 – b2 – a – b = (a2 – b2) – (a + b) = (a – b)(a + b) – (a + b) = (a + b)(a – b – 1); б) 3c – 3d + c2 – d2 = (3c – 3d) + (c2 – d2) = 3(c – d) + (c – d)(c + d) = (c – d)(3 + c + d); в) 5a – 2c – 25a2 + 4c2 = 5a – 2c – (25a2 – 4c2) = (5a – 2c) – (5a – 2c) • (5a + 2c) = (5a – 2c)(1 – 5a – 2c); г) x2 + y – y2 + x = x2 – y2 + (x + y) = (x – y)(x + y) + (x + y) = (x + y)(x – y + 1); ґ) x3 – a3 + x – a = (x – a)(x2 + xa + a2) + (x + a) = (x – a)(x2 + xa + a2 + 1); д) a + b – a3 – b3 = (a + b) – (a3 + b3) = (a + b) – (a + b) • (a2 – ab + b2) = (a + b) • (1 – (a2 – ab + b2) = (a + b)(1 – a2 + ab – b2).