- 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 $(ax+by)^2+(bx-ay)^2$.
The given algebraic expression is $(ax+by)^2+(bx-ay)^2$.
We have to factorize the expression $(ax+by)^2+(bx-ay)^2$.
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 $(ax+by)^2+(bx-ay)^2$ by grouping similar terms and taking out the common factors.
We can write $(ax+by)^2+(bx-ay)^2$ as,
$(ax+by)^2+(bx-ay)^2=(ax)^2+2(ax)(by)+(by)^2+(bx)^2-2(bx)(ay)+(ay)^2$ [Since $(m+n)^2=m^2+2mn+n^2$ and $(m-n)^2=m^2-2mn+n^2$]
The terms in the given expression are $a^2x^2, b^2y^2, b^2x^2$ and $a^2y^2$.
We can group the given terms as $a^2x^2, b^2x^2$ and $b^2y^2, a^2y^2$.
Therefore, by taking $x^2$ as common in $a^2x^2, b^2x^2$ and $y^2$ as common in $b^2y^2, a^2y^2$, we get,
Now, taking $(a^2+b^2)$ common, we get,
Hence, the given expression can be factorized as $(x^2+y^2)(a^2+b^2)$.
Kickstart Your Career
Get certified by completing the courseGet Started