x³(x-2y)+y³(2x-y)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 16:14:08

x³(x-2y)+y³(2x-y)
x³(x-2y)+y³(2x-y)

x³(x-2y)+y³(2x-y)
原式=x^4-2x³y+2xy²-y^4
=(x^4-y^4)-(2x³y-2xy³)
=(x²+y²)(x²-y²)-2xy(x²-y²)
=(x²-y²)(x²-2xy+y²)
=(x+y)(x-y)³

x³(x-2y)+y³(2x-y)
=(x^4-y^4)-(2x³y-2xy³)
=(x²+y²)(x²-y²)-2xy(x²-y²)
=(x²-y²)(x²-2xy+y²)
=(x+y)(x-y)³

x³(x-2y)+y³(2x-y)=X^4-2X^3y+2xy^3-y^4
=(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)(x-Y)(X-y)

原式=X^4-2X^3Y+2XY^3-Y^4
=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^2-Y^2)(X-Y)^2