On factorising 3m2n+12mn+12n, we get the factor(s) as:
3
m+2
The expression 3m2n+12mn+12n can be written as
3×m×m×n+3×2×2×m×n+3×2×2×n....(i)
Taking 3n as the common factor from (i), we get
=3n(m2+4m+4)...(ii)
Comparing (m2+4m+4) with the identity (a2+2ab+b2)=(a+b)2, we get
a2=m2⇒a=m...(iii)
b2=22⇒b=2...(iv)
⇒3n(m2+4m+4)=3n(m+2)2=3n(m+2)(m+2)
Therefore, the factors of 3m2n+12mn+12n are 3n ,(m+2) and (m+2).
i.e., 3m2n+12mn+12n=3n(m+2)(m+2)