Factorize the expression $x^3-144x$.

Given:

The given expression is $x^3-144x$.

To do:

We have to factorize the expression $x^3-144x$.

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.

$x^3-144x$ can be written as,

$x^3-144x=x(x^2-144)$

$x^3-144x=x[(x)^2-(12)^2]$             [Since $144=(12)^2$]

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,

$x^3-144x=x[(x)^2-(12)^2]$

$x^4-144x=x(x+12)(x-12)$

Hence, the given expression can be factorized as $x(x+12)(x-12)$.

Akhileshwar Nani

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Updated on: 07-Apr-2023

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