Factorize the expression $xa^2+xb^2-ya^2-yb^2$.

Given:

The given algebraic expression is $xa^2+xb^2-ya^2-yb^2$.

To do:

We have to factorize the expression $xa^2+xb^2-ya^2-yb^2$.

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.

Here, we can factorize the expression $xa^2+xb^2-ya^2-yb^2$ by grouping similar terms and taking out the common factors. 

The terms in the given expression are $xa^2, xb^2, -ya^2$ and $-yb^2$.

We can group the given terms as $xa^2, xb^2$ and $-ya^2, -yb^2$. 

Therefore, by taking $x$ as common in $xa^2, xb^2$ and $-y$ as common in $-ya^2, -yb^2$, we get,

$xa^2+xb^2-ya^2-yb^2=x(a^2+b^2)-y(a^2+b^2)$

Now, taking $(a^2+b^2)$ common, we get,

$xa^2+xb^2-ya^2-yb^2=(x-y)(a^2+b^2)$

Hence, the given expression can be factorized as $(x-y)(a^2+b^2)$.

Akhileshwar Nani

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Updated on: 05-Apr-2023

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