Rút gọn biểu thức: P = 12.(5^2+1)(5^4+1)(5^8+1)(5^16+1)

* Hướng dẫn giải

$\begin{array}{l}\mathrm{P}=12.\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\\ 2\mathrm{P}=24.\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\\ =\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\\ =\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)=\mathrm{.....}=5^{32}-1\\ \Rightarrow \mathrm{P}=\frac{5^{32}-1}{2}\end{array}$