Question

因式分解题目(高中难度)

Answer 1

1.1999X^2-(1999^2-1)X-1999=1999X*(X-1999)+X-1999=(X-1999)*(1999X+1)
提示：可以将1999换为Y就很好做了！！
2.(X+Y-2XY)(X+Y-2)+(XY-1)^2=(X+Y)^2-2X-2Y-2X^Y-2YX^2+4XY+(XY-1)^2=(X+Y)^2-2X(XY+1)-2Y(XY+1)+(XY+1)^2=(X+Y)^2-2(X+Y)(XY+1)+(XY+1)^2=(X+Y-XY-1)^2=(X-1)^2(Y-1)^2
提示：对于这类式子应先拆再合(X+Y)^2-2X(XY+1)-2Y(XY+1)+(XY+1)^2
这一步注意整体合并！
3.(2X-3Y)^3+(3X-2Y)^3-125(X-Y)^3=（5X-5Y)((2X-3Y)^2-(3X-2Y)(2X-3Y)+(3X-2Y)^2)-(5X-5Y)^3=
-5(X-Y)(18X^2+18Y^2-39XY)=-15(X-Y)(2X-3Y)(3X-2Y)
提示：注意用x^3+y^3=(x+y)(x^2-xy+y^2)和
x^3-y^3=(x-y)(x^2+xy+y^2)