Question

Rút gọn: 12.(5^2+1).(5^4+1).(5^8+1)(.5^16+1)

Giúp tớ với

Answer 1

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

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

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

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

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

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

Vậy \(A=\frac{5^{32}-1}{2}\)

Answer 2

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

=\(\frac{12.\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{24}\)

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

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

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