Доведіть тотожність:
а) (а + 2)(а2 – 2а – 3) = (а – 3)(а2 + 3а + 2);
б) (a + b)(b – c) – (a – b)(b + c) = 2(b2 – ac).
а) (а + 2)(а2 – 2а – 3) = (а – 3)(а2 + 3а + 2);
б) (a + b)(b – c) – (a – b)(b + c) = 2(b2 – ac).
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Ответ:а)(a + 2)(a - 2) - (a - 3)(a² + 3a + 9) = a(a² - 4) - (a³ - 3³) = a³ - 4a - a³ + 27 =
= 27 - 4aб)a2-ac+2ab+b2-bc/ab-c2+ac+b2 =
=a2+2ab-ac+b2-bc/ab+ac+b2-c2 =
=(a+b)(a+b-c)/(b+c)(a+b-c) =
=a+b/b+c in
Объяснение: