分解因式:(1).x2(x-1)-4(1-x)2 (2),(a+b)(a+b-6)+9 (3)、(x2+1)2-4(x2+1)+4

问题描述:

分解因式:(1).x2(x-1)-4(1-x)2 (2),(a+b)(a+b-6)+9 (3)、(x2+1)2-4(x2+1)+4

(1).x^2(x-1)-4(1-x)^2=x^2(x-1)-4(x-1)^2= (x-1)[x^2-4(x-1)]=(x-1)(x-2)^2(2),(a+b)(a+b-6)+9 =(a+b)^2-6(a+b)+9=(a+b-3)^2(3)(x^2+1)^2-4(x^2+1)+4=[(x^2+1)-2]^2=(x^2-1)^2=(x+1)^2(x-1)^2