因式分解:(1)3ax^2-3ay^.(2)(2X一3y)^一(3x一2y)^.(3)x^(y^一1)+(1一y^).(4)(X^一6)^一6(X^一6)+9..
问题描述：
因式分解:(1)3ax^2-3ay^.(2)(2X一3y)^一(3x一2y)^.(3)x^(y^一1)+(1一y^).(4)(X^一6)^一6(X^一6)+9..
答
(1)3ax^2-3ay^。
=3a(x²-y²)
=3a(x+y)(x-y)
(2)(2X一3y)^2一(3x一2y)^2。
=(2x-3y+3x-2y)(2x-3y-3x+2y)
=(5x-5y)(-x-y)
=-5(x-y)(x+y)
(3)x^2(y^2一1)+(1一y^2)。
=(y²-1)(x²-1)
=(y+1)(y-1)(x+1)(x-1)
(4)(X^2一6)^2一6(X^2一6)+9
=(x²-6-3)²
=(x²-9)²
=(x+3)²(x-3)²
答
(1)3ax²-3ay²=3a(x²-y²)=3a(x+y)(x-y)(2)(2X一3y)²一(3x一2y)²=[(2x-3y)+(3x-2y)][(2x-3y-(3x-2y)]=(2x-3y+3x-2y)(2x-3y-3x+2y)=(5x-5y)(-x-y)=-5(x-y)(x+y)(3)x²(y²一1)+(...