factorize

( x^2 + y^2 - 2xy ) + ( x - y - 6 )
=( x - y )^2 + ( x - y ) - 6
=( x - y - 2 ) ( x - y +3 ) (ANS.)

2006-12-23 20:22:57 補充：
Take x - y = z, we have( x^2 + y^2 - 2xy ) + ( x - y - 6 )=( x - y )^2 + ( x - y ) - 6=z^2 + z - 6=( z - 2) ( z +3)=( x - y - 2 ) ( x - y +3 ) (ANS.)Common mistake:(x-y)^2 + (x-y-6) = (x-y)(x-y-6)which is absolutely incorrect.

(x^2+y^2-2xy) + (x-y-6)
= (x-y)^2 + (x-y) - 6
= [(x-y) +3] [(x-y) -2]
= (x-y+3)(x-y-2)

(x^2+y^2-2xy) + (x-y-6)
= (x-y)^2 + (x-y) - 6
= [(x-y) +3] [(x-y) -2]
= (x-y+3)(x-y-2)

(x^2+y^2-2xy)+(x-y-6)
= (x-y)^2 + (x-y-6)
= (x-y)(x-y-6)

factorize
(x^2+y^2-2xy)+(x-y-6)
=x^2+y^2-2xy)+x-y-6
=x^2+x+y^2-y-2xy-6
=x(x+1)+y(y-1)-2(xy-3),,