Factorize the expression $x^5-16x^3$.

Given:

The given algebraic expression is $x^5-16x^3$.

To do:

We have to factorize the expression $x^5-16x^3$.

Solution:

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. 

Therefore,

$x^5-16x^3=x^3[(x)^2-(4)^2]$

$x^5-16x^3=x^3(x+4)(x-4)$

Hence, the given expression can be factorized as $x^3(x+4)(x-4)$.

Akhileshwar Nani

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Updated on: 08-Apr-2023

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