Розділ 2. РОЗКЛАДАННЯ МНОГОЧЛЕНІВ » 640

Розклади на множники многочлен. a) (2a + 3)2 – (n – 1)2 = (2a + 3 – (n – 1))(2a + 3 + n – 1) = (2a + 3 – n + 1)(2a + n + 2) = (2a – n + 4) • (2a + n + 2); б) 4(x – y)2 – (x + y)2 = (2(x – y) – (x + y)) • (2(x – y) + x + y) = (2x – 2y + x + y) = (x – 3y)(3x – y); в) a2 – 2ac + c2 – x2 – 2x – 1 = (a – c)2 – (x2 + 2x + 1) = (a – c)2 – (x + 1)2 = (a – c – (x + 1))(a – c + x + 1) = (a – c – x – 1)(a – c + x + 1); г) c2 + 4ac + 4a2 – m2 + 2mn – n2 = (c + 2a)2 – (m2 – 2mn + n2) = (c – 2a)2 – (m – n)2 = (c + 2a – (m – n))(c + 2a + m – n) = (c + 2a – m + n)(c + 2a + m – n).