Вправи 501 - 595 » 519

Розкладіть на множники вираз: 1) a2 – 3 = a2 – (√3)2 = (a – √3)(a + √3); 2) 4b2 – 2 = (2b)2 – (√2)2 = (2b – √2)(2b + √2); 3) a – 9 = (√a) – 32 = (√a – 3)( √a + 3); 4) m – n = (√m)2 – (√n)2 = (√m – √n)( √m + √n); 5) 16x – 25y = (4√x)2 – (5√y)2 = (4√x – 5√y)(4√x + 5√y); 6) a – 2√a + 1 = (√a)2 – 2√a + 12 = (√a – 1)2; 7) 4m – 28√mn + 49n = (2√m)2 – 28√mn + (7√n)2 = (2√m – 7√n)2; 8) b + 6√b + 9 = (√b)2 + 6√b + 32 = (√b + 3)2; 9) 3 + 2√3c + c = (√3)2 + 2√3c + (√c)2 = (√3 + √c)2; 10) 2 + √2 = (√2)2 + √2 = √2(√2 + 1); 11) 6√7 – 7 = 6√7 – (√7)2 = √7(6 – √7); 12) a – √a = (√a)2 – √a = √a(√a – 1); 13) √b + √3b = √b + √3 • √b = √b(1 + √3); 14) √15 – √5 = √5 • √3 – √5 = √5(√3 – 1).