Преобразуйте в многочлен: (2^3n + 4^n + 2^n + 1)(2^n

sobakazabiyaka (2^3n+4^n+2^n+1)(2^n-1)+1
2^4n-2^3n+8^n-4^n+2^2n-2^n+2^n-1+1
16^n-8^n+8^n-4^n+4^n
16^n

1 votes Thanks 1

noorajensen18 спасибо

terinariy $\left(2^{3n}+4^n+2^n+1\right)\left(2^n-1\right)+1 = \left(2^n+4^n+8^n+1\right)\left(2^n-1\right)+1= \\ =\left(8^n+4^n+2^n+1\right)\left(2^n-1\right)= \\ =16^n-8^n+8^n-4^n+2^2^n-2^n+2^n-1= 16^n-4^n+4^n-1= \\=16^n-1=16^n-1+1=16^n$

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