分解因式 :1.（x^-2x）^-2(x^-2x)-3

题目

分解因式 :1.（x^-2x）^-2(x^-2x)-3
2.(a+1)x^+(a+1)X-6a-6
3.a^+b^-1-2ab
4.(x+Y)^-2(x^-y^)+(x-y)^
5.-（a-b）^-(b-a)的三次方

答案

1.（x^-2x）^-2(x^-2x)-3
＝(x²-2x-3)(x²-2x+1)
=(x-3)(x+1)(x-1)²
2.(a+1)x^+(a+1)X-6a-6
=x(a+1)(x+1)-6(a+1)
=(a+1)[x(x+1)-6]
=(a+1)(x²+x-6)
=(a+1)(x+3)(x-2)
3.a^+b^-1-2ab
=(a²-2ab+b²)-1
=(a-b)²-1
=(a-b+1)(a-b-1)
4.(x+Y)^-2(x^-y^)+(x-y)^
=(x+y)²-2(x+y)(x-y)+(X-y)²
=[(x+y)-(x-y)]²
=(x+y-x+y)²
=(2y)²
5.-（a-b）^-(b-a)的三次方
=-(b-a)²-(b-a)³
=(b-a)²[-1-(b-a)]
=(b-a)²(a-b-1)