用乘法公式计算 1999^2-2000*1998
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用乘法公式计算 1999^2-2000*1998
计算(2+1)(2^2+1)(2^4+1)...(2^32+1)写出计算步骤
计算(2+1)(2^2+1)(2^4+1)...(2^32+1)写出计算步骤
![用乘法公式计算 1999^2-2000*1998](/uploads/image/z/1118248-16-8.jpg?t=%E7%94%A8%E4%B9%98%E6%B3%95%E5%85%AC%E5%BC%8F%E8%AE%A1%E7%AE%97+1999%5E2-2000%2A1998)
1999^2-2000*1998
=1999²-(1999+1)(1999-1)
=1999²-1999²+1
=1
(2+1)(2^2+1)(2^4+1)...(2^32+1)
=(2-1)(2+1)(2^2+1)(2^4+1)...(2^32+1)
=(2^2-1)(2^2+1)(2^4+1)...(2^32+1)
=(2^4-1)(2^4+1)...(2^32+1)
=……
=(2^32-1)(2^32+1)
=2^64-1
=1999²-(1999+1)(1999-1)
=1999²-1999²+1
=1
(2+1)(2^2+1)(2^4+1)...(2^32+1)
=(2-1)(2+1)(2^2+1)(2^4+1)...(2^32+1)
=(2^2-1)(2^2+1)(2^4+1)...(2^32+1)
=(2^4-1)(2^4+1)...(2^32+1)
=……
=(2^32-1)(2^32+1)
=2^64-1