作业帮因式分解:(1)3ax^2-3ay^.(2)(2X一3y)^一(3x一2y)^.(3)x^(y^一1)+(1一y^).(
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/18 03:51:06
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..
(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)+(1一y²)
=x²(y²-1)-(y²-1)
=(y²-1)(x²-1)
=(y+1)(y-1)(x+1)(x-1)
(4)(X²一6)²一6(X²一6)+9
=[(x²-6)-3]²
=(x²-9)²
=(x+3)²(x-3)²
=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)+(1一y²)
=x²(y²-1)-(y²-1)
=(y²-1)(x²-1)
=(y+1)(y-1)(x+1)(x-1)
(4)(X²一6)²一6(X²一6)+9
=[(x²-6)-3]²
=(x²-9)²
=(x+3)²(x-3)²
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