高一的因式分解,急..

来源：百度知道 编辑：UC知道 时间：2024/05/24 08:37:10
(X-2Y)X^3-(Y-2X)Y^3
X^3-9X+8
X^4+4
能做几道就说几道 真的很急的 谢谢

(X-2Y)X^3-(Y-2X)Y^3
=x^4-2x^3y-y^4+2xy^3
=(x^4-y^4)-2xy(x^2-y^2)
=(x^2+y^2)(x^2-y^2)-2xy(x^2-y^2)
=(x^2-y^2)(x^2+y^2-2xy)
=(x+y)(x-y)^3

x^3-9x+8
=x^3-1-9x+9
=(x-1)(x^2+x+1)-9(x-1)
=(x-1)(x^2+x-8)
其中求解x^2+x-8=0得到两根x1,x2
则
x^3-9x+8=(x-1)(x-x1)(x-x2)

x^4+4
=x^4+4x^2-4x^2+4
=(x^2+2)^2-(2x)^2
=(x^2-2x+2)(x^2+2x+2)

(X-2Y)X^3-(Y-2X)Y^3
=X^4-2X^3Y-Y^4+2XY^3
=(X^4-Y^4)-2XY(X^2-Y^2)
=(X^2-Y^2)(X^2+Y^2-2XY)
=(X+Y)(X-Y)^3
X^3-9X+8
=X^3-X^2+X^2-9X+8
=X^2(X-1)+(X-1)(X-8)
=(X-1)(X^2+X-8)

第一个我和你们的好像不一样·
(X-2Y)X^3-(Y-2X)Y^3
=X^4-2XY^3-Y^4+2XY^3
=-2XY(X^2-Y^2)+X^4-Y^4
=-2XY(X^2-Y^2)+(X^2+Y^2)(X^2-Y^2)
=(X^2-2XY+Y^2)*(X^2-Y^2)
=[(X^2-Y^2)]^2