分解因式(1)x^2-2x(2)ay^2+2ay+a(3)4a^2-8ab^2+12ab(4)a^2b(a-b)+6ab(b-a)(5)x^5-9xy^5(6)(x-1)(x-2)+1/4(7)(x^2+4)^2-16x^2(8)6x^2+11x-7

Question

分解因式
(1)x^2-2x (2)ay^2+2ay+a (3)4a^2-8ab^2+12ab
(4)a^2b(a-b)+6ab(b-a) (5)x^5-9xy^5 (6)(x-1)(x-2)+1/4
(7)(x^2+4)^2-16x^2 (8)6x^2+11x-7

Answer 1

(1)x^2-2x=x(x-2)
(2)ay^2+2ay+a=a(y^2+2y+1)=a(y+1)^2
(3)4a^2-8ab^2+12ab=4a(a-2b^2+3b)
(4)a^2b(a-b)+6ab(b-a)=(a-b)(a^2b-6ab)=ab(a-b)(a-6)
(5)x^5-9xy^5=x(x^4-9y^5)
(6)(x-1)(x-2)+1/4=x^2-3x+9/4=(x-3/2)^2
(7)(x^2+4)^2-16x^2=(x^2+4+4x)(x^2+4-4x)=(x+2)^2(x-2)^2
(8)6x^2+11x-7=(2x-1)(3x+7)