Factorize the expression $256x^3-81x$.

Given:

The given expression is $256x^3-81x$.

To do:

We have to factorize the expression $256x^3-81x$.

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.

$256x^3-81x$ can be written as,

$256x^3-81x=x(256x^2-81)$             (Taking $x$ common)

$256x^3-81x=x[(16x)^2-(9)^2]$             [Since $256=(16)^2, 81=(9)^2$]

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,

$256x^3-81x=x[(16x)^2-(9)^2]$

$256x^3-81x=x(16x+9)(16x-9)$

Hence, the given expression can be factorized as $x(16x+9)(16x-9)$.

Akhileshwar Nani

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Updated on: 08-Apr-2023

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