Question

Use the formula to find the factors.

(11) $\frac{16}{25}-\frac{y^2}{x^2}$

Answer 1

$$\begin{gathered} \frac{16}{25}-\frac{y^2}{x^2} \\ ={\left(\frac{4}{5}\right)}^2-{\left(\frac{y}{x}\right)}^2 \\ =\left(\frac{4}{5}+\frac{y}{x}\right)\left(\frac{4}{5}-\frac{y}{x}\right)\left[a^2-b^2=\left(a+b\right)\left(a-b\right)\right] \\ \therefore \frac{16}{25}-\frac{y^2}{x^2}=\left(\frac{4}{5}+\frac{y}{x}\right)\left(\frac{4}{5}-\frac{y}{x}\right) \end{gathered}$$