Question

ÏÈÔĶÁÏÂÃæµÄ²ÄÁÏ£¬ÔÙ·Ö½âÒòʽ£º

    Òª°Ñ¶àÏîʽam+an+bm+bn·Ö½âÒòʽ£¬¿ÉÒÔÏÈ°ÑËüµÄÇ°Á½Ïî·Ö³ÉÒ»×飬²¢Ìá³öa£»°ÑËüµÄºóÁ½Ïî·Ö³ÉÒ»×飬²¢Ìá³öb£¬´Ó¶øµÃµ½a£¨m+n£©+b£¨m+n£©£®Õâʱ£¬ÓÉÓÚa£¨m+n£©+b£¨m+n£©ÓÖÓй«Òòʽ£¨m+n£©£¬ÓÚÊÇ¿ÉÌṫÒòʽ£¨m+n£©£¬´Ó¶øµÃµ½£¨m+n£©£¨a+b£©£®Òò´ËÓÐam+an+bm+bn=£¨am+an£©+£¨bm+bn£©=a£¨m+n£©+b£¨m+n£©=£¨m+n£©£¨a+b£©£®

    ÕâÖÖÒòʽ·Ö½âµÄ·½·¨½Ð×ö·Ö×é·Ö½â·¨£®Èç¹û°ÑÒ»¸ö¶àÏîʽµÄÏî·Ö×é²¢Ìá³ö¹«Òòʽºó£¬ËüÃǵÄÁíÒ»¸öÒòʽÕýºÃÏàͬ£¬ÄÇôÕâ¸ö¶àÏîʽ¾Í¿ÉÒÔÀûÓ÷Ö×é·Ö½â·¨À´·Ö½âÒòʽÁË£®

    ÇëÓÃÉÏÃæ²ÄÁÏÖÐÌṩµÄ·½·¨·Ö½âÒòʽ£º

    £¨1£©a²£­ab+ac£­bc£»    £¨2£©m²+5n£­mn£­5m£®

Answer 1

½â£º£¨1£©a²£­ab+ac£­bc=£¨a²£­ab£©+£¨ac£­bc£©

=a£¨a£­b£©+c£¨a£­b£©=£¨a£­b£©£¨a+c£©£®

£¨2£©m²+5n£­mn£­5m=£¨m²£­mn£©+£¨5n£­5m£©

=m£¨m£­n£©+5£¨n£­m£©=m£¨m£­n£©£­5£¨m£­n£©=£¨m£­n£©£¨m£­5£©£®