3x2+4xy-y2因式分解2x(x-y)4-x2(x-y)2+xy((y-x)2x3-13x-12x3+2x2+2x+

(2x+y)(x-y)-4x-5y-6
=(2x+y+2)(x-y-3)

2x(x-y)^4 - x²(x-y)² + xy(y-x)²
=2x(x-y)^4 - x²(x-y)² + xy(x-y)²
=x(x-y)^2[2(x-y)² - x + y]
=x(x-y)^2[2(x-y)² - (x-y)]
=x(x-y)^2*(x-y)[2(x-y)-1]
=x(x-y)^3[2(x-y)-1]
=x(x-y)^3(2x-2y-1)

有理数范围不能分解
实数范围
原式=(2x²-4x+2)-1
=(√2x-√2)²-1
=(√2x-√2+1)(√2x-√2-1)

2x³-4x²y³+6x²y²
=2x²(x-2y³+3y²)

2x²-x=x(2x-1)

2x²-4x+2=2（x²-2x+1）=2（x-1）²