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Factorize the expression $x^5-16x^3$.
The given algebraic expression is $x^5-16x^3$.
We have to factorize the expression $x^5-16x^3$.
Factorizing algebraic expressions:
Factorizing an algebraic expression implies 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.
$x^5-16x^3$ can be written as,
$x^5-16x^3=x^3(x^2-16)$ (Taking $x^3$ common)
$x^5-16x^3=x^3[(x)^2-(4)^2]$ [Since $16=(4)^2$]
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.
Hence, the given expression can be factorized as $x^3(x+4)(x-4)$.
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