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Factorize the expression $18a^2x^2-32$.
Given:
The given expression is $18a^2x^2-32$.
To do:
We have to factorize the expression $18a^2x^2-32$.
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.
$18a^2x^2-32$ can be written as,
$18a^2x^2-32=2(9a^2x^2-16)$ (Taking $2$ common)
$18a^2x^2-32=2[(3ax)^2-(4)^2]$ [Since $9a^2x^2=(3ax)^2, 16=4^2$]
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,
$18a^2x^2-32=2[(3ax)^2-(4)^2]$
$18a^2x^2-32=2(3ax+4)(3ax-4)$
Hence, the given expression can be factorized as $2(3ax+4)(3ax-4)$.
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