Question

1.Rút gọn biểu thức 

A=(2+1)(2^2+1)(2^4+1)......(2^256+1)

Answer 1

\(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{256}+1\right)\)

      \(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{256}+1\right)\)

      \(=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{256}+1\right)\)

      \(=\left(2^8-1\right)\left(2^8+1\right)....\left(2^{256}+1\right)\)

         .........................................................

        \(=\left(2^{256}-1\right)\left(2^{256}+1\right)\)

         \(=\left[\left(2^{256}\right)^2-1^2\right]\)

           \(=2^{512}-1\)