\(A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8\)
\(=\left(2+2^2\right)+\left(2^3+2^4\right)+\left(2^5+2^6\right)+\left(2^7+2^8\right)\)
\(=2\left(1+2\right)+2^3\left(1+2\right)+2^5\left(1+2\right)+2^7\left(1+2\right)\)
\(=\left(1+2\right)\left(2+2^3+2^5+2^7\right)\)
\(=3\left(2+2^3+2^5+2^7\right)\)\(⋮\)\(3\)