100X100一99X99+98X98一97X97+,十2X2一1X1

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100X100一99X99+98X98一97X97+,十2X2一1X1100X100一99X99+98X98一97X97+,十2X2一1X1100X100一99X99+98X98一97X97+,十2X

100X100一99X99+98X98一97X97+,十2X2一1X1
100X100一99X99+98X98一97X97+,十2X2一1X1

100X100一99X99+98X98一97X97+,十2X2一1X1
100的平方减99的平方=(100+99)(100-99)=100+99,把其他的项也按这样的方式分解,上面的式子就变成:
100+99+98+97+.+2+1=5050