Вправи 501 - 600 » 598

Розкладіть на множники, користуючись формулою різниці квадратів: 1) (х + 2)2 – 49 = (х + 2 – 7)(х + 2 + 7) = (х – 5)(х + 9); 2) (х – 10)2 – 25y2 = (х – 10 – 5у)(х – 10 + 5у) – (х – 5у – 10)(х + 5у – 10); 3) 25 – (у – З)2 = (5 – (у–3))(5 + (у – 3)) = (5 – у + 3)(5 + у – 3) = (8 – у)(2 + у); 4) (а – 4)2 – (a + 2)2 = (а – 4 – (а + 2))(а – 4 + (a + 2)) = (а – 4 – a – 2)(а – 4 + а + 2) = –6(2a – 2) = –12(a – 1); 5) (m – 10)2 – (n – 6)2 = (m – 10 – (n – 6))(m – 10 + (n – 6)) = (m – 10 – n + 6)(m – 10 + n – 6 ) = (m – n – 4 )(m + n – 16); 6) (8у + 4)2 – (4у – З)2 = (8у + 4 – (4у – 3))(8у + 4 + (4у – 3)) = (8у + 4 – 4у + 3)(8у + 4 + 4у – 3) = (4у + 7)(12у + 1); 7) (5a + Зb)2 – (2a – 4b)2 = (5а + Зb – (2а – 4b))(5а + Зb +(2а – 4b)) = (5a + 3b – 2а + 4b)(5a + 3b + 2a – 4b) = (За + 7b)(7a – b); 8) 4(a – b)2 – (а + b)2 = (2(a – b))2 – (a + b)2 = (2(a – b) –(a + b))(2(a – b) + (а + b)) = (2а – 2b – а – b)(2а – 2b + а + b) = (a – 3b)(3а – b); 9) (х2 + х + 1)2 – (х2 – х + 2)2 = (х2 + х + 1 – (х2 – х + 2))(х2 + х +1 + (х2 – х + 2)) = (х2 + х + 1 – х2 + х – 2)(х2 + х + 1 + х2 – х + 2) = (2х – 1)(2х2 + 3); 10) (–Зх3 + у)2 – 16х6 = (–Зх3 + у)2 – (4х3)2 = (–Зх3 + у – 4х3)(–Зх3 + у + 4х3) = (–7x3 + у)(х3 + у).