Question

这四道题 麻烦解答下 因式分解

Answer 1

1、(1-x²)(1-y²)-4xy
=1-x²-y²+x²y²-4xy
=(x²y²-2xy+1)-(x²+2xy+y²)
=(xy-1)²-(x+y)²
=(xy+x+y-1)(xy-x-y-1)
2、a²-b²+4a+2b+3
=(a²+4a+4)-(b²-2b+1)
=(a+2)²-(b-1)²
=(a+2+b-1)(a+2-b+1)
=(a+b+1)(a-b+3)
3、x³+x²y-xy²-4x+4y-y³
=(x³-y³)+(x²y-xy²)-(4x-4y)
=(x-y)(x²+xy+y²)+xy(x-y)-4(x-y)
=(x-y)(x²+2xy+y²-4)
=(x-y)[(x+y)²-2²)
=(x-y)(x+y+2)(x+y-2)
4、x²-4a²+8ab-4b²
=x²-4(a²-2ab+b²)
=x²-4(a-b)²
=(x+2a-2b)(x-2a+2b)