Question

Rút gon biểu thức:

P=12(5²+1)(5⁴+1)(5⁸+1)(5¹⁶+1)

Answer 1

Ta có:

P=12(5²+1)(5⁴+1)(5⁸+1)(5¹⁶+1)

P=(5²-1)(5²+1)(5⁴+1)(5⁸+1)(5¹⁶+1):2

P=(5^4-1)(5⁴+1)(5⁸+1)(5¹⁶+1):2

P=(5^8-1)(5⁸+1)(5¹⁶+1):2

P=(5¹⁶-1)(5¹⁶+1):2

P=(5³²-1):2

Answer 2

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

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

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

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

\(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)=\frac{5^{32}-1}{2}\)