Question

Use the formula to find the factors.

(10) $\frac{r^2}{s^2}-\frac{81}{100}$

Answer 1

$$\begin{gathered} \frac{r^2}{s^2}-\frac{81}{100} \\ ={\left(\frac{r}{s}\right)}^2-{\left(\frac{9}{10}\right)}^2 \\ =\left(\frac{r}{s}+\frac{9}{10}\right)\left(\frac{r}{s}-\frac{9}{10}\right)\left[a^2-b^2=\left(a+b\right)\left(a-b\right)\right] \\ \therefore \frac{r^2}{s^2}-\frac{81}{100}=\left(\frac{r}{s}+\frac{9}{10}\right)\left(\frac{r}{s}-\frac{9}{10}\right) \end{gathered}$$