X2Y2_X2_Y2+4XY+1
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X2Y2_X2_Y2+4XY+1
X2Y2_X2_Y2+4XY+1
X2Y2_X2_Y2+4XY+1
解题原理:利用(a-b)^2=a^2+b^2-2ab和(a+b)*(a-b)=a^2-b^2这2个常用公式,把4xy拆成2个2xy形式,从而凑出公式,最后化简.这种“凑”的方法在今后高中数学解题的时候经常用到,是一种必须掌握的技巧
详见如下:
x2y2-x2-y2+4xy+1
=(x2y2+2xy+1)-(x2+y2-2xy)
=(xy+1)2-(x-y)2
=[(xy+1)+(x-y)]*[(xy+1)-(x-y)]
=(xy+x-y+1)(xy-x+y+1)
为便于书写,解答方式采用了你的书写形式.
x^2y^2-x^2-y^2+4xy+1
=x^2y^2+2xy+1-x^2-y^2+2xy
=(xy)^2+2xy+1-(x^2+y^2-2xy)
=(xy+1)^2-(x-y)^2
=(xy+1-x+y)(xy+1+x-y)
注意:x^2表示x的平方,依次类推。
x^2y^2-x^2-y^2+4xy+1
=x^2y^2+2xy+1-(x^2-2xy+y^2)
=(xy+1)^2-(x-y)^2
=(xy+x-y+1)(xy-x+y+1)
把4xy拆开成2个2xy
成为两个完全平方
(xy+1)^-(x-y)^
然后平方差
(xy+1+x-y)(xy+1-x+y)
以x为主
x2(y2-1)+4xy+(1-y2)
十字相乘法
(x(y+1)+(1-y))*(x(y-1)+(1+y))=(xy+x-y+1)(xy-x+y+1)
I don't know
X2Y2_X2_Y2+4XY+1
=(x^2y^2+2xy+1)-(x^2-2xy+y^2)
=(xy+1)^2-(x-y)^2
=(xy+1+x-y)(xy+1-x+y)