Question

On factorising $3m^{2}n+12mn+12n$, we get the factor(s) as:

• A. 3
• B. m+2
• C. m+3
• D. All the above

Answer 1

Answer: (A), (B)

The correct options are
A

3

B

m+2

The expression $3m^{2}n+12mn+12n$ can be written as

$3\times m\times m\times n+3\times 2\times 2\times m\times n+3\times 2\times 2\times n$....(i)

Taking $3n$ as the common factor from (i), we get

$=3n(m^2+4m+4)$...(ii)

Comparing $(m^2+4m+4)$ with the identity $(a^2+2ab+b^2)=(a+b{)}^2$, we get

$a^2=m^2\Rightarrow a=m$...(iii)

$b^2=2^2\Rightarrow b=2$...(iv)

$\Rightarrow 3n(m^2+4m+4)$$=3n(m+2{)}^2=3n(m+2\left)\right(m+2)$

Therefore, the factors of $3m^{2}n+12mn+12n$ are $3n$ ,$(m+2)$ and $(m+2)$.

i.e., $3m^{2}n+12mn+12n=3n(m+2)(m+2)$