- 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 $x^3-2x^2y+3xy^2-6y^3$.
The given algebraic expression is $x^3-2x^2y+3xy^2-6y^3$.
We have to factorize the expression $x^3-2x^2y+3xy^2-6y^3$.
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.
Here, we can factorize the expression $x^3-2x^2y+3xy^2-6y^3$ by grouping similar terms and taking out the common factors.
The terms in the given expression are $x^3, -2x^2y, 3xy^2$ and $-6y^3$.
We can group the given terms as $x^3, 3xy^2$ and $-2x^2y, -6y^3$.
Therefore, by taking $x$ as common in $x^3, 3xy^2$ and $-2y$ as common in $-2x^2y, -6y^3$, we get,
Now, taking $(x^2+3y^2)$ common, we get,
Hence, the given expression can be factorized as $(x-2y)(x^2+3y^2)$.
Kickstart Your Career
Get certified by completing the courseGet Started