(2 +1)(2 в кв +1)(2в 4 +1)(2 в 16+1)(2 в 32+1)=?упростить выражение

Решите задачу:

$(2+1)*(2^2+1)*(2^4+1)*(2^8+1)(2^{16}+1}*(2^{32}+1))=\\\\(2-1)(2+1)*(2^2+1)*(2^4+1)*(2^8+1)(2^{16}+1}*(2^{32}+1))=\\\\(2^2-1)*(2^2+1)*(2^4+1)*(2^8+1)(2^{16}+1}*(2^{32}+1))=\\\\(2^4-1)*(2^4+1)*(2^8+1)(2^{16}+1}*(2^{32}+1))=\\\\(2^8-1)*(2^8+1)(2^{16}+1}*(2^{32}+1))=\\\\(2^{16}-1)*(2^{16}+1}*(2^{32}+1))=\\\\(2^{32}-1)*(2^{32}+1))=\\\\2^{64}-1$