第一题：（x + y - 2xy)(x + y - 2 )+(xy-1）²
=(x+y)^2-2xy(x+y)-2(x+y)+4xy+(xy)^2-2xy+1
=(x+y)^2-2(xy+1)(x+y)+(xy+1)^2 (注:这里设x+y=a,xy+1=b,可能容易理解些)
=[(x+y)-(xy+1)]^2
=[(x-1)(y-1)]^2
=(x-1)^2*(y-1)^2
第二题：（x +1)(x+2)(x+3)(x+6)+x²
= [(x+1)(x+6)][(x+2)(x+3)]+x^2
=(x^2+6+7x)(x^2+6+5x)+x^2
=(x^2+6)^2+12x(x^2+6)+35x^2+x^2
=(x^2+6)^2+2*6x(x^2+6)+(6x)^2
=(x^2+6+6x)^2
=(x^2+6x+6)^2
第三题：9x²-15xy-6y²=3(3x²-5xy-2y²)
=3(3x+y)(x-2y)
=3*2007/3*8/2007
=8