求这几道因式分解,
问题描述：
求这几道因式分解,
1.4A^-9B^+C^-4AC
2.(AX+BY)^+(BX-AY)^
3.X^(X-Y)+(Y-X)
4.(X-3)(X-1)+1
5.P(X-Y)-Q(Y-X)
6.(X+Y)^-(Y+X)
注：＾为平方的意思
答
1.4A^-9B^+C^-4AC =(2A-C)^2-9B^2=(2A-C+3B)(2A-C-3B)
2.(AX+BY)^+(BX-AY)^=(A^2+B^2)x^2+( A^2+B^2)Y^2=(A^2+B^2)(X^2+Y^2)
3.X^(X-Y)+(Y-X)=x^2(x-y)-(x-y)=(x-y)(x+1)(x-1)
4.(X-3)(X-1)+1=x^2-4x+3+1=(x-2)^2
5.P(X-Y)-Q(Y-X)= P(X-Y)+Q(X-Y)=(X-Y)(P+Q)
6.(X+Y)^-(Y+X)=(X+y)(X+Y-1)