Question

因式分解：x的平方乘以y的平方+xy-x的平方-y的平方+x+y+2

因为我不会输平方，所以有点麻烦哈

Answer 1

我用x^2表示x的平方
x^2y^2+xy-x^2-y^2+x+y+2
=x^2y^2-x^2-y^2+1+xy+x+y+1
=(x^2-1)(y^2-1)+(x+1)(y+1)
=(x+1)(x-1)(y+1)(y-1)+(x+1)(y+1)
=(x+1)(y+1)(xy-x-y+1)+(x+1)(y+1)
=(x+1)(y+1)(xy-x-y+2)

Answer 2

先如此分割
x²y²-x²-y²+1+xy+x+y+1
=（x²-1）（y²-1）+（x+1)(y+1)
=（x+1)(y+1)(xy-x-y+2)

Answer 3

x^y^+xy-x^-y^+x+y+2
=x^y^-x^-y^+1+xy+x+y+1
=(x^-1)(y^-1)+(x+1)(y+1)
=(x+1)(x-1)(y^-1)+(x+1)(y+1)
同理...
=(x+1)(y+1)[(x-1)(y-1)+1]
=(x+1)(y+1)(xy-x-y+2)