因式分解:X(X-1)+Y(Y+1)-2XY

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因式分解:X(X-1)+Y(Y+1)-2XY因式分解:X(X-1)+Y(Y+1)-2XY因式分解:X(X-1)+Y(Y+1)-2XYX(X-1)+Y(Y+1)-2XY=X^2-2XY+Y^2-(X-Y

因式分解:X(X-1)+Y(Y+1)-2XY
因式分解:X(X-1)+Y(Y+1)-2XY

因式分解:X(X-1)+Y(Y+1)-2XY
X(X-1)+Y(Y+1)-2XY=X^2-2XY+Y^2-(X-Y)=(X-Y)^2-(X-Y)=(X-Y)(X-Y-1)

展开是
原式= x^2 -x + y^2 +y -2xy = (x^2-2xy+y^2) -(x-y) = (x-y)^2 -(x-y) = (x-y)(x-y-1);