运用乘法公式计算(2+1)(2^2 +1)(2^4+1)(2^8+1)(2^16+1)+1的值

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运用乘法公式计算(2+1)(2^2 +1)(2^4+1)(2^8+1)(2^16+1)+1的值

(2-1)(2+1)(2^2 +1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^2-1)(2^2 +1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^8-1)(2^8+1)(2^16+1)+1
=(2^16-1))(2^16+1)+1
=2^32-1+1
=2^32

(2+1)(2^2 +1)(2^4+1)(2^8+1)(2^16+1)+1
=1*(2+1)(2^2 +1)(2^4+1)(2^8+1)(2^16+1)+1
=(2-1)(2+1)(2^2 +1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^2-1)(2^2 +1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^8-1)(2^8+1)(2^16+1)+1
=(2^16-1)(2^16+1)+1
=2^32-1+1
=2^32