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ab(a+b)²-(a+b)² +1
=(ab-1)(a+b)²+1
=(ab-1)a²+(ab-1)b²+2ab(ab-1)+1
=(ab-1)a²+(ab-1)b²+2(ab)²-2ab+1
=(ab-1)a²+(ab-1)b²+(ab)²+(ab)²-2ab+1
=(ab-1)a²+(ab-1)b²+(ab)²+(ab²-2ab+1)
=(ab-1)a²+(ab-1)b²+(ab)²+(ab-1)²
=[(ab-1)a²+(ab)²]+[(ab-1)b²+(ab-1)²]
=a²[(ab-1)+b²]+(ab-1)*[(ab-1)+b²]
=(a²+ab-1)(b²+ab-1)
=(ab-1)(a+b)²+1
=(ab-1)a²+(ab-1)b²+2ab(ab-1)+1
=(ab-1)a²+(ab-1)b²+2(ab)²-2ab+1
=(ab-1)a²+(ab-1)b²+(ab)²+(ab)²-2ab+1
=(ab-1)a²+(ab-1)b²+(ab)²+(ab²-2ab+1)
=(ab-1)a²+(ab-1)b²+(ab)²+(ab-1)²
=[(ab-1)a²+(ab)²]+[(ab-1)b²+(ab-1)²]
=a²[(ab-1)+b²]+(ab-1)*[(ab-1)+b²]
=(a²+ab-1)(b²+ab-1)
参考资料： http://zhidao.baidu.com/question/170725695.html
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