因式分解:(1)-16a^3(b-c)+24a(b-c)^2 (2)25(m-n)^3-15(n-m)^2 (3)(c-d)^2-c+d (4)81(a-b)^2-36(b-a直接写答案就行了.谢谢谢(4)81(a-b)^2-36(b-a )

问题描述:

因式分解:(1)-16a^3(b-c)+24a(b-c)^2 (2)25(m-n)^3-15(n-m)^2 (3)(c-d)^2-c+d (4)81(a-b)^2-36(b-a
直接写答案就行了.谢谢谢
(4)81(a-b)^2-36(b-a )

(1)-16a^3(b-c)+24a(b-c)^2
=8a(b-c)[3(b-c)-2a^2]
=8a(b-c)(3b-3c-2a^2)
(2)25(m-n)^3-15(n-m)^2
=25(m-n)^3-15(m-n)^2
=5(m-n)^2[5(m-n)-3]
=5(m-n)^2(5m-5n-3)
(3)(c-d)^2-c+d
=(c-d)^2-(c-d)
=(c-d)(c-d-1)
(4)81(a-b)^2-36(b-a )
=81(a-b)^2+36(a-b )
=9(a-b)[9(a-b )+4]
=9(a-b)(9a-9b +4)