Вправи 501 - 595 » 513

Виконайте множення: 1) (2 – √3)( √3 + 1) = 2√3 + 2 – (√3)2 – √3 = 2√3 + 2 – 3 – √3 = √3 – 1; 2) (√2 + √5)(2√2 – √5) = 2(√2)2 – √2 • √5 + 2√2 • √5 – (√5)2 = 2 • 2 – √10 + 2√10 – 5 = √10 – 1; 3) (a + √b)(a – √b) = a2 – (√b)2 = a2 – b; 4) (√b – √c)( √b + √c) = (√b)2 – (√c)2 = b – c; 5) (4 + √3)(4 – √3) = 42 – (√3)2 = 16 – 3 = 13; 6) (y – √7)(y + √7) = y2 – (√7)2 = y2 – 7; 7) (4√2 – 2√3)(2√3 + 4√2) = (4√2)2 – (2√3) = 16 • 2 – 4 • 3 = 32 – 12 = 20; 8) (m + √n)2 = m2 + 2m√n + (√n)2 = m2 + 2m√n + n; 9) (√a – √b)2 = (√a)2 – 2√a • √b + (√b)2 = a – 2√ab + b; 10) (2 – 3√3)2 = 22 – 2 • 3√3 + (3√3)2 = 4 – 6√3 + 9 • 3 = 4 – 6√3 + 27 = 31 – 6√3.