Question

Tính giá trị của biểu thức:
D= 9.(10+1)(10²+1)(10⁴+1)(10⁸+1)(10¹⁶+1)

Answer 1

\(D=\left(10-1\right)\left(10+1\right)\left(10^2+1\right)\left(10^4+1\right)\left(10^8+1\right)\left(10^{16}+1\right)\)

\(=\left(10^2-1\right)\left(10^2+1\right)\left(10^4+1\right)\left(10^8+1\right)\left(10^{16}+1\right)\)

\(=\left(10^4-1\right)\left(10^4+1\right)\left(10^8+1\right)\left(10^{16}+1\right)\)

\(=\left(10^8-1\right)\left(10^8+1\right)\left(10^{16}+1\right)\)

\(=\left(10^{16}-1\right)\left(10^{16}+1\right)\)

\(=10^{32}-1\)