Question
Factorise $\frac{1}{36} a^2 b^2-\frac{16}{49} b^2 c^2$.
✓
Answer
We have,
$
\begin{array}{l}
\frac{1}{36} a^2 b^2-\frac{16}{49} b^2 c^2 \\
=b^2\left(\frac{a^2}{36}-\frac{16 c^2}{49}\right)=b^2\left(\frac{a^2}{6 \times 6}-\frac{4 \times 4}{7 \times 7} c^2\right) . \\
=b^2\left[\left(\frac{a}{6}\right)^2-\left(\frac{4 c}{7}\right)^2\right] \\
=b^2\left(\frac{a}{6}+\frac{4 c}{7}\right)\left(\frac{a}{6}-\frac{4 c}{7}\right) \quad \text { [using Identity III] }
\end{array}
$
$
\begin{array}{l}
\frac{1}{36} a^2 b^2-\frac{16}{49} b^2 c^2 \\
=b^2\left(\frac{a^2}{36}-\frac{16 c^2}{49}\right)=b^2\left(\frac{a^2}{6 \times 6}-\frac{4 \times 4}{7 \times 7} c^2\right) . \\
=b^2\left[\left(\frac{a}{6}\right)^2-\left(\frac{4 c}{7}\right)^2\right] \\
=b^2\left(\frac{a}{6}+\frac{4 c}{7}\right)\left(\frac{a}{6}-\frac{4 c}{7}\right) \quad \text { [using Identity III] }
\end{array}
$
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