Question
Multiply: $\big(\frac{\text{x}}{7}+\frac{\text{x}^2}{2}) \ \text{by}\big(\frac{2}{5}+\frac{9\text{x}}{4}\big)$
✓
Answer
To multiply, we will use distributive law as follows:$\big(\frac{\text{x}}{7}+\frac{\text{x}^2}{2}) \ \text{by}\big(\frac{2}{5}+\frac{9\text{x}}{4}\big)$
$=\frac{\text{x}}{7}\big(\frac{2}{5}+\frac{9\text{x}}{4}\big)+\frac{\text{x}^2}{2}\big(\frac{2}{5}+\frac{9\text{x}}{4}\big)$
$=\frac{2\text{x}}{35}+\frac{9\text{x}^2}{28}+\frac{\text{x}^2}{5}+\frac{9\text{x}^3}{8}$
$=\frac{2\text{x}}{35}+\big(\frac{45+28}{140}\big)\text{x}^2+ \frac{9\text{x}^3}{8}$
$=\frac{2x}{35}+\frac{73\text{x}^2}{140} +\frac{9\text{x}^2}{8}$
Thus, the answer is $\frac{2x}{35}+\frac{73\text{x}^2}{140} +\frac{9\text{x}^2}{8}.$
$=\frac{\text{x}}{7}\big(\frac{2}{5}+\frac{9\text{x}}{4}\big)+\frac{\text{x}^2}{2}\big(\frac{2}{5}+\frac{9\text{x}}{4}\big)$
$=\frac{2\text{x}}{35}+\frac{9\text{x}^2}{28}+\frac{\text{x}^2}{5}+\frac{9\text{x}^3}{8}$
$=\frac{2\text{x}}{35}+\big(\frac{45+28}{140}\big)\text{x}^2+ \frac{9\text{x}^3}{8}$
$=\frac{2x}{35}+\frac{73\text{x}^2}{140} +\frac{9\text{x}^2}{8}$
Thus, the answer is $\frac{2x}{35}+\frac{73\text{x}^2}{140} +\frac{9\text{x}^2}{8}.$
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