- Trending Categories
- Data Structure
- Operating System
- MS Excel
- C Programming
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Factorize the expression $256x^3-81x$.
The given expression is $256x^3-81x$.
We have to factorize the expression $256x^3-81x$.
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.
Hence, the given expression can be factorized as $x(16x+9)(16x-9)$.
Kickstart Your Career
Get certified by completing the courseGet Started