Question

x²y²+xy-x²-y²+x+y+2因式分解,

Answer 1

x²y²+xy-x²-y²+x+y+2

=(x²y²-x²-y²+1)+(xy+x+y+1)

=[x²(y²-1)-(y²-1)]+[x(y+1)+(y+1)]

=(x²-1)(y²-1)+(x+1)(y+1)

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

=(x+1)(y+1)[(x-1)(y-1)+1]

=(x+1)(y+1)(xy-x-y+2)