Question

因式分解:4mn^2-4m^2n-n^3 16m^2-4(m+n)^2 (x^2-6)^2-6(x^2-6)+9 x^2

Answer 1

4mn^2-4m^2n-n^3

=n(4mn-4m^2-n^2)

=-n(n-2m)^2

16m^2-4(m+n)^2

=4(2m+m+n)(2m-m-n)

=4(3m+n)(m-n)

(x^2-6)^2-6(x^2-6)+9

=(x^2-6-3)^2

=(x^2-9)^2

=(x+3)^2(m-3)^2

x^2(x-y)+y^2(y-x)

=x^2(x-y)-y^2(x-y)

=(x-y)(x^2-y^2)

=(x-y)^2(x+y)

(x+y)^2-4xy

=x^2+2xy+y^2-4xy

=x^2-2xy+y^2

=(x-y)^2