Выполни умножение: (5-1) ⋅ (5+1) ⋅ (5^2+1) ⋅ (5^4+1) ⋅ (5^8+1) - 5^16+22

Question

Алгебра

Маруха

25 апреля, 20:10

Выполни умножение: (5-1) ⋅ (5+1) ⋅ (5^2+1) ⋅ (5^4+1) ⋅ (5^8+1) - 5^16+22

+3

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Петрята · Answer 1

(5-1) ⋅ (5+1) ⋅ (5^2+1) ⋅ (5^4+1) ⋅ (5^8+1) - 5^16+22 = 5 ¹⁶-1-5¹⁶+22=21

решим (5-1) ⋅ (5+1) ⋅ (5^2+1) ⋅ (5^4+1) ⋅ (5^8+1) = (5²-1) (5²+1) (5⁴+1) (5⁸+1) = (5⁴-1) (5⁴+1) (5⁸+1) = (5⁸-1) (5⁸+1) = 5¹⁶-1

a²-b² = (a-b) (a+b)