Find the following products:
$ \frac{-4}{27} x y z\left[\frac{9}{2} x^{2} y z-\frac{3}{4} x y z^{2}\right] $
Given:
\( \frac{-4}{27} x y z\left[\frac{9}{2} x^{2} y z-\frac{3}{4} x y z^{2}\right] \)
To do:
We have to find the given product.
Solution:
$\frac{-4}{27} x y z[\frac{9}{2} x^{2} y z-\frac{3}{4} x y z^{2}] =(\frac{-4}{27} x y z \times \frac{9}{2} x^{2} y z)+(\frac{-4}{27} x y z \times \frac{-3}{4} x y z^{2})$
$=\frac{-2}{3} x^{1+2} \times y^{1+1} \times z^{1+1}+\frac{1}{9} x^{1+1} \times y^{1+1} \times z^{1+2}$
$=\frac{-2}{3} x^{3} y^{2} z^{2}+\frac{1}{9} x^{2} y^{2} z^{3}$
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