Question

Rút gọn biểu thức 

P=12(5²+1)(5⁴+1)(5^8+1)(5^16+1)

Cảm ơn

Answer 1

\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(=\frac{\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\frac{\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\frac{\left(5^8-1\right)\left(5^8+1\right)}{2}=\frac{\left(5^{16}-1\right)\left(5^{16}+1\right)}{2}\)

\(=\frac{5^{32}-1}{2}\)