幫我做因式分解

幫你做功課? 見你一條咁少就教o下你啦

x^2y^2+x^2y-xy^2-3xy-x+y+1

= (xy)(xy) - xy + x(xy) - y(xy) - xy + 1 - xy - x + y

= (xy)(xy) - (1- x)xy - (y + 1)xy + (1 - x)(y + 1)

= (xy - (y+1))(xy - (1-x))


2008-06-10 05:53:51 補充：
Yes, the reasoning is correct.
My 1st step is writing the expression in terms of xy.

think...
in order to have x²y² term
the possible combinations are...
a) (x²y²+...)(1+...)
b) (x²y+...)(y+...)
c) (xy²+...)(x+...)
d) (xy+...)(xy+...)
the most possible form is (d) as xy term can be formed after expressing

So, we try....
x²y² + x²y - xy² - 3xy - x + y + 1 = (xy + Ax + B)(xy + Cy + D)
.......................= x²y² + Ax²y + Cxy² + (B+D+AC)xy + ADx + BCy + BD
compare the coefficents
we have A = 1 and C = -1
AD = -1 so D = -1
BC = 1 so B = -1

so, x²y² + x²y - xy² - 3xy - x + y + 1 = (xy + x - 1)(xy - y - 1)