Question

因式分解题

X^3-X^2Y-XY^2+Y^3 能用3次方的公式吗？ 详细 谢谢
要解题 过程

Answer 1

X^3-X^2Y-XY^2+Y^3
=X^3+Y^3-XY(X+Y)
=(X+Y)(X^2-XY+Y^2)-XY(X+Y)
=(X+Y)(X^2-2XY+Y^2)
=(X+Y)(X-Y)^2

Answer 2

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

Answer 3

X^3-X^2Y-XY^2+Y^3
=X^2(X-Y)+Y^2(X-Y)
=(X^2+Y^2)(X-Y)
X^3+Y^3=(X+Y)(X^2-XY+Y^2)
无法直接用三次方公式

Answer 4

X^3-X^2Y-XY^2+Y^3=(X^3-X^2Y)-（XY^2-Y^3）
=X^2(X-Y)-Y^2(X-Y)=(X-Y)(X^2-Y^2)=(X+Y)(X-Y)^2