(1-m)(1-m)(6-m)+18+18-9(1-m)-4(6-m)-9(1-m)怎么提公因式?_数学解答

(1-m)(1-m)(6-m)+18+18-9(1-m)-4(6-m)-9(1-m)怎么提公因式?

人气：387 ℃　时间：2020-10-01 07:36:47

解答

=(1-m)^2(6-m)-4(6-m)-18(1-m)+36
=(6-m)[(1-m)^2-4]-18[(1-m)-2]
=(6-m)[(1-m)+2][(1-m)-2]+18(m+1)
=(6-m)(3-m)[-(m+1)]+18(m+1)
=(m+1)[18-(6-m)(3-m)]
=(m+1)(9m-m^2)
=m(m+1)((9-m)