因式分解题1.-3a^3b-6a^2b^2+9ab2.(a^2+b^2-c^2)^2-4a^2b^23.4(x+y)^2-20(x+y)+254.(1-a)mn+a-15.1/4x+x^3-x^2

Question

因式分解题
1.-3a^3b-6a^2b^2+9ab
2.(a^2+b^2-c^2)^2-4a^2b^2
3.4(x+y)^2-20(x+y)+25
4.(1-a)mn+a-1
5.1/4x+x^3-x^2

Answer 1

1.-3a^3b-6a^2b^2+9ab
=-3ab(a^2+2a-3)
=-3ab(a+3)(a-1)
2.(a^2+b^2-c^2)^2-4a^2b^2
=(a^2+b^2-c^2)^2-(2ab)^2
[平方差公式]
=(a^2+b^2-c^2-2ab)(a^2+b^2-c^2+2ab)
=[(a-b)^2-c^2][(a+b)^2-c^2]
=(a-b-c)(a-b+c)(a+b-c)(a+b+c)
3.4(x+y)^2-20(x+y)+25
=[2(x+y)]^2-20(x+y)+5^2
=(2(x+y)-5)^2
=(2x+2y-5)^2
4.(1-a)mn+a-1
=(1-a)mn-(1-a)
=(1-a)(mn-1)
5.1/4x+x^3-x^2
=x(x^2-x+1/4)
=x(x-1/2)^2