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Factorize the expression $12m^2-27$.
Given:
The given expression is $12m^2-27$.
To do:
We have to factorize the expression $12m^2-27$.
Solution:
Factorizing algebraic expressions:
Factorizing an algebraic expression means writing the expression as a product of two or more factors. Factorization is the reverse of distribution.
An algebraic expression is factored completely when it is written as a product of prime factors.
$12m^2-27$ can be written as,
$12m^2-27=3[4m^2-9]$ (Taking $3$ as common)
$12m^2-27=3[(2m)^2-(3)^2]$ [Since $4=2^2, 9=3^2$]
Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression.
Therefore,
$12m^2-27=3[(2m)^2-(3)^2]$
$12m^2-27=3(2m+3)(2m-3)$
Hence, the given expression can be factorized as $3(2m+3)(2m-3)$.
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