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Multiply:
\( \left(\frac{x}{7}+\frac{x^{2}}{2}\right) \) by \( \left(\frac{2}{5}+\frac{9 x}{4}\right) \)
To do:
We have to multiply \( \left(\frac{x}{7}+\frac{x^{2}}{2}\right) \) by \( \left(\frac{2}{5}+\frac{9 x}{4}\right) \)
Solution:
We know that,
$(a+b)\times(c+d)=a(c+d)+b(c+d)$
Therefore,
$(\frac{x}{7}+\frac{x^{2}}{2}) \times(\frac{2}{5}+\frac{9 x}{4})=\frac{x}{7}(\frac{2}{5}+\frac{9 x}{4})+\frac{x^{2}}{2}(\frac{2}{5}+\frac{9 x}{4})$
$=\frac{2 x}{35}+\frac{9}{28} x^{2}+\frac{x^{2}}{5}+\frac{9 x^{3}}{8}$
$=\frac{2}{35} x+\frac{45 x^{2}+28 x^{2}}{140}+\frac{9 x^{3}}{8}$
$=\frac{2}{35} x+\frac{73}{140} x^{2}+\frac{9}{8} x^{3}$
$=\frac{9}{8} x^{3}+\frac{73}{140} x^{2}+\frac{2}{35} x$
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