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Question

On factorising 3m2n+12mn+12n, we get the factor(s) as:


A

3

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B

m+2

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C

m+3

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D

All the above

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Solution

The correct options are
A

3


B

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=m2a=m...(iii)

b2=22b=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)


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