(2+1)(2平方+1)(2四次方+1)(2八次方+1)简便计算
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![(2+1)(2平方+1)(2四次方+1)(2八次方+1)简便计算](/uploads/image/z/392669-53-9.jpg?t=%EF%BC%882%2B1%EF%BC%89%EF%BC%882%E5%B9%B3%E6%96%B9%2B1%EF%BC%89%EF%BC%882%E5%9B%9B%E6%AC%A1%E6%96%B9%2B1%EF%BC%89%EF%BC%882%E5%85%AB%E6%AC%A1%E6%96%B9%2B1%EF%BC%89%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97)
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(2+1)(2平方+1)(2四次方+1)(2八次方+1)简便计算
(2+1)(2平方+1)(2四次方+1)(2八次方+1)简便计算
(2+1)(2平方+1)(2四次方+1)(2八次方+1)简便计算
利用平方差公式
(2+1)*(2^2+1)*(2^4+1)*(2^8+1)
=(2-1)(2+1)*(2^2+1)*(2^4+1)*(2^8+1)
=(2^2-1)*(2^2+1)*(2^4+1)*(2^8+1)
=(2^4-1)*(2^4+1)*(2^8+1)
=(2^8-1)*(2^8+1)
=2^16 -1
=65536-1
=65535
3*5*17*257=65535