(m+n)^2+4m+4n+4m^2如何分解因式

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(m+n)^2+4m+4n+4m^2如何分解因式
(m+n)^2+4m+4n+4m^2如何分解因式

(m+n)^2+4m+4n+4m^2如何分解因式
(m+n)^2+4m+4n+4m^2
=5m^2+(4+2n)m+(n^2+4n)
令5m^2+(4+2n)m+(n^2+4n)=0
△=(4+2n)^2-4*5*(n^2+4n)= -16n^2-64n+16
m= [-(4+2n)±√△]/10
所以
(m+n)^2+4m+4n+4m^2
=5(m+((n+2+2√(-n^2-4n+1))/5)*(m+((n+2)-2√(-n^2-4n+1))/5)