Question

Use the formula to find the factors.

(12) $1-\frac{36m^2}{49n^2}$

Answer 1

$$\begin{gathered} 1-\frac{36m^2}{49n^2} \\ ={\left(1\right)}^2-{\left(\frac{6m}{7n}\right)}^2 \\ =\left(1+\frac{6m}{7n}\right)\left(1-\frac{6m}{7n}\right)\left[a^2-b^2=\left(a+b\right)\left(a-b\right)\right] \\ \therefore 1-\frac{36m^2}{49n^2}=\left(1+\frac{6m}{7n}\right)\left(1-\frac{6m}{7n}\right) \end{gathered}$$