Выполни умножение: (5−1)⋅(5+1)⋅(5^2+1)⋅(5^4+1)⋅(5^8+1)−5^16+31

Question

Алгебра: Выполни умножение: (5−1)⋅(5+1)⋅(5^2+1)⋅(5^4+1)⋅(5^8+1)−5^16+31

богдан1703 · Answer

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