Answer
10 (a). $ (x - y) (x + y) (x^{2} + y^{2})$
10 (b). $ (\sin\theta - \cos\theta) (\sin\theta + \cos\theta) $
Work Step by Step
10 (a). Given expression is-
$ x^{4} - y^{4}$
= $ (x^{2})^{2} - (y^{2})^{2}$
= $ (x^{2} - y^{2}) (x^{2} + y^{2})$
= $ (x - y) (x + y) (x^{2} + y^{2})$
{Recall $a^{2} - b^{2}$ = (a-b)(a+b)}
10 (b).
Given expression is-
$ \sin^{4}\theta - \cos^{4}\theta$
= $ (\sin^{2}\theta)^{2} - (\cos^{2}\theta)^{2}$
= $ (\sin^{2}\theta - \cos^{2}\theta) (\sin^{2}\theta + \cos^{2}\theta)$
= $ \sin^{2}\theta - \cos^{2}\theta $
{As $\sin^{2}\theta + \cos^{2}\theta = 1$}
= $ (\sin\theta - \cos\theta) (\sin\theta + \cos\theta) $
{Recall $a^{2} - b^{2}$ = (a-b)(a+b)}
