试将下列各式分解因式x²-(a+b)xy+aby²xy-1+x-y2x²+xy-y²-4x+5y-6

Question

试将下列各式分解因式
x²-(a+b)xy+aby²
xy-1+x-y
2x²+xy-y²-4x+5y-6

Answer 1

x²-(a+b)xy+aby²
=x²-axy-bxy+aby²
=x²-axy-(bxy-aby²)
=x(x-ay)-by(x-ay)
=(x-ay)(x-by) (提公因式法)

xy-1+x-y
=xy-y+x-1
=y(x-1)+x-1
=(x-1)(y+1)(提公因式法)

2x²+xy-y²-4x+5y-6