Розділ 2. РОЗКЛАДАННЯ МНОГОЧЛЕНІВ » 559

Розклади на множники. a) (a – 3)2 – 4 = (a – 3)2 – 22 = (a – 3 – 2)(a – 3 + 2) = (a – 5)(a – 1); б) (x + 5)2 – 16y2 = (x + 5)2 – (4y)2 = (x + 5 – 4y) • (x + 5 + 4y) = (x – 4y + 5)(x + 4y + 5). в) (3n + 5)2 – (2n – 1)2 = (3n + 5 – (2n – 1)) • (3n + 5 + 2n – 1) = (3n + 5 – 2n + 1)(5n + 4) = (n + 6)(5n + 4); г) (m – 6)2 – (m + 7)2 = (m – 6 – (m + 7))(m – 6 + m + 7) = (m – 6 – m – 7)(2m + 1) = –13(2m + 1).