Розділ 2. РОЗКЛАДАННЯ МНОГОЧЛЕНІВ » 560

Розклади на множники. a) (p + 6)2 – 16 = (p + 6)2 – 42 = (p + 6 – 4)(p + 6 + 4) = (p + 2)(p + 10); б) (a – 7)2 – 25c2 = (a – 7)2 – (5c)2 = (a – 7 – 5c) • (a – 7 + 5c) = (a – 5c – 7)(a + 5c – 7); в) (2x – 5y)2 – (6x + y)2 = (2x – 5y – (6x + y)) • (2x – 5y + 6x + y) = (2x – 5y – 6x – y)(8x – 4y) = (–4x – 6y)(8x – 4y); г) (a – 9)2 – (a + 5)2 = (a – 9 – (a + 5))(a – 9 + a + 5) = (a – 9 – a – 5)(2a – 4) = –14(2a – 4).