1,4x^2-4x-y^2+4y-3
问题描述：
1,4x^2-4x-y^2+4y-3
2,(x+y-2xy)(x+y-2)+(xy-1)^2
3,4x^3-31x+15
4,x^3+5x^2+3x-9
5,(x^4-4x^2+1)(x^4+3x^2+1)+10x^4
答
1,4x^2-4x-y^2+4y-3
=(4X平方-4X+1)-(Y平方-4Y+4)
=(2X-1)平方-(Y-2)平方
=(2X+Y-3)(2X-Y+1)
2,(x+y-2xy)(x+y-2)+(xy-1)^2
=(X+Y)平方-2(XY+1)(X+Y)+4XY+(XY+1)平方-4XY
=(X+Y-XY-1)平方
3,4x^3-31x+15
=(4X立方-36X)+(5X+15)
=4X(X+3)(X-3)+5(X+3)
=(X+3)(4X平方-12X+5)
=(X+3)(2X-5)(2X-1)
4,x^3+5x^2+3x-9
=(X立方+4X平方+3X)+(X平方-9)
=X(X+1)(X+3)+(X+3)(X-3)
=(X+3)(X平方+2X-3)
=(X+3)(X-1)(X+3)
=(X-1)(X+3)平方
5,(x^4-4x^2+1)(x^4+3x^2+1)+10x^4
设X平方=Y
原式=(Y平方-4Y+1)(Y平方+3Y+1)+10Y平方
=Y四次-X立方-Y+1
=Y立方(Y-1)-(Y-1)
=(Y-1)(Y立方-1)
=(Y-1)平方(Y平方+Y+1)
=(X+1)平方(X-1)平方(X四次+X平方+1)