Factorize each of the following expressions:

$x a^{2}+x b^{2}-y a^{2}-y b^{2}$

$=\left(x a^{2}+x b^{2}\right)-\left(y a^{2}+y b^{2}\right)$           [Grouping the expressions]

$=x\left(a^{2}+b^{2}\right)-y\left(a^{2}+b^{2}\right)$

$=(x-y)\left(a^{2}+b^{2}\right)$          $\left[\right.$ Taking $\left(a^{2}+b^{2}\right)$ as the common factor $]$