Question:
Factorize each of the following expressions:
xa2 + xb2 − ya2 − yb2
Solution:
$x a^{2}+x b^{2}-y a^{2}-y b^{2}$
$=\left(x a^{2}+x b^{2}\right)-\left(y a^{2}+y b^{2}\right)$ [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 $]$
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