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Question
Factorize each of the following expression:
\[\frac{1}{16} x^2 y^2 - \frac{4}{49} y^2 z^2\]
Solution
\[\frac{1}{16} x^2 y^2 - \frac{4}{49} y^2 z^2 \]
\[ = y^2 \left( \frac{1}{16} x^2 - \frac{4}{49} z^2 \right)\]
\[ = y^2 \left[ \left( \frac{1}{4}x \right)^2 - \left( \frac{2}{7}z \right)^2 \right]\]
\[ = y^2 \left( \frac{1}{4}x - \frac{2}{7}z \right)\left( \frac{1}{4}x + \frac{2}{7}z \right)\]
\[ = y^2 \left( \frac{x}{4} - \frac{2}{7}z \right)\left( \frac{x}{4} + \frac{2}{7}z \right)\]
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