問題詳情:
閱讀材料:把代數式x2﹣6x﹣7因式分解,可以如下分解:
x2﹣6x﹣7
=x2﹣6x+9﹣9﹣7
=(x﹣3)2﹣16
=(x﹣3+4)(x﹣3﹣4)
=(x+1)(x﹣7)
(1)探究:請你仿照上面的方法,把代數式x2﹣8x+7因式分解;
(2)拓展:把代數式x2+2xy﹣3y2因式分解:
當= 時,代數式x2+2xy﹣3y2=0.
【回答】
【解答】解:(1)x2﹣8x+7
=x2﹣8x+16﹣16+7
=(x﹣4)2﹣32
=(x﹣4+3)(x﹣4﹣3)
=(x﹣1)(x﹣7)
(2)x2+2xy﹣3y2
=x2+2xy+y2﹣y2﹣3y2
=(x+y)2﹣4y2
=(x+y+2y)(x+y﹣2y)
=(x+3y)(x﹣y),
當=﹣3或1時,x2+2xy﹣3y2的值爲0.
知識點:因式分解
題型:解答題