Question

【计算，分解因式】x²(x-y)+y²(y-x)

Answer 1

原式=(x^2-y^2)(x-y)
=(x+y)(x-y)^2

追问

若x²+y²-6y+4x+13=0,则x²-y ²=？？

追答

x^2+y^2-6y+4x+13=0
(x+2)^2+(y-3)^2=0
x+2=y-3=0
x=-2 y=3
所以x^2-y^2=4-9=-5

Answer 2

x²(x-y)+y²(y-x)
=(x-y)(x² - y²)
=(x-y)(x-y)(x+y)
=(x-y)²(x+y)

追问

若x²+y²-6y+4x+13=0,则x²-y ²=？

追答

x²+y²-6y+4x+13=0
化简左边为（x+2)² + (y-3)²=0，所以x+2=0,y-3=0;
解得x= -2,y=3
x²-y ²=4-9=-5

Answer 3

x²(x-y)+y²(y-x) = x²(x-y)-y²(x-y) = (x²-y²)(x-y)=(x+y)(x-y)(x-y)

追问

若x²+y²-6y+4x+13=0,则x²-y ²=？

追答

x²+y²-6y+4x+13 = (x²+4x + 4) + (y²-6y+9) = (x+2)² + (y-3)² = 0
于是x=-2 y= 3
所以x²-y ² = 4-9 = -5