因式分解1.9（a+b）^2+12(a+b)+4 2.(a^3+4a^2+4a)÷(a^2+2a) 3.3(y-x)^2+2(x-y)

题目

因式分解1.9（a+b）^2+12(a+b)+4 2.(a^3+4a^2+4a)÷(a^2+2a) 3.3(y-x)^2+2(x-y)

答案

1、9(a+b)^2+12(a+b)+4
=[3(a+b)]^2+12(a+b)+2^2
=[3(a+b)+2]^2
=(3a+3b+2)^2
2、(a^3+4a^2+4a)÷(a^2+2a)
=a(a^2+4a+4)÷a(a+2)
=a(a+2)^2÷a(a+2)
=a+2
3、3(y-x)^2+2(x-y)
=3(x-y)^2+2(x-y)
=(x-y)[3(x-y)+2]
=(x-y)(3x-3y+2)