Question

x(x+y)(x-y)-x(x+y)² 这道题的解法能在具体些吗？拜托拜托！~

Answer 1

原式=x[(x+y)(x-y)-(x+y)² ]
=x[x-²y²(-x²+2xy+y²)]
=x(-2y²-2xy)
=-2xy(x+y)

Answer 2

X (X + Y) (X - Y) - X (X + Y)^2
= X (X + Y) [ (X - Y) - (X + Y) ]
= X (X + Y) (- 2Y)
= -2 (X + Y) X Y
= - 2X^2 Y - 2XY^2

Answer 3

x(x+y)(x-y)-x(x+y)²
=x(x^2-y^2)-x(x^2+2xy+y^2)
=x^3-xy^2-(x^3+2x^2y+xy^2)
=x^3-xy^2-x^3-2x^2y-xy^2
=-2xy^2-2x^2y

追问

貌似错了，不过提醒了我！谢谢~O(∩_∩)O~

追答

（x+y）（x-y）=x^2-y^2(平方差公式)
(x+y)²=x^2+2xy+y^2（完全平方和公式）
x(x+y)(x-y)-x(x+y)²
=x(x^2-y^2)-x(x^2+2xy+y^2)
=x^3-xy^2-(x^3+2x^2y+xy^2)
=x^3-xy^2-x^3-2x^2y-xy^2
=-2xy^2-2x^2y
应该没有问题啊！！

追问

呵呵，可能吧！不过我们现在学的是提取公因式法，你还去合并它...有点复杂！
x(x+y)(x-y)-x(x+y)²
=x(x+y) [（x-y)-(x+y) ]
=x(x+y)(-2y)
-2xy(x+y)
⊙﹏⊙b汗..我一时头脑短路，把它弄复杂了！~

追答

x(x+y)(x-y)-x(x+y)² 这道题
若是化简：
=-2xy^2-2x^2y

若是分解因式：
=-2xy^2-2x^2y
=-2xy(x+y)

Answer 4

x[(x+y)(x-y)-(x+y)²]
=x(x²-y²-x²-2xy-y²)
=-x(2xy+2y²)
=-2xy(x+y)
=-2x²y-2xy²