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Factorize the expression $27x^2-12y^2$.
The given expression is $27x^2-12y^2$.
We have to factorize the expression $27x^2-12y^2$.
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.
$27x^2-12y^2$ can be written as,
$27x^2-12y^2=3[9x^2-4y^2]$ (Taking $3$ as common)
$27x^2-12y^2=3[(3x)^2-(2y)^2]$ [Since $9=3^2, 4=2^2$]
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.
Hence, the given expression can be factorized as $3(3x+2y)(3x-2y)$.
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