Question

Factorize each of the following expression:
$\frac{1}{16}{x}^2{y}^2-\frac{4}{49}{y}^2{z}^2$

Answer 1

$$\begin{gathered} \frac{1}{16}{x}^2{y}^2-\frac{4}{49}{y}^2{z}^2 \\ =y^2\left(\frac{1}{16}{x}^2-\frac{4}{49}{z}^2\right) \\ =y^2\left[{\left(\frac{1}{4}x\right)}^2-{\left(\frac{2}{7}z\right)}^2\right] \\ =y^2\left(\frac{1}{4}x-\frac{2}{7}z\right)\left(\frac{1}{4}x+\frac{2}{7}z\right) \\ =y^2\left(\frac{x}{4}-\frac{2}{7}z\right)\left(\frac{x}{4}+\frac{2}{7}z\right) \end{gathered}$$