Verify that (11 p q+4 q)^2-(11 p q-4 q)^2=176 p q^2 - Vidyadip

Question

Verify that
$(11 p q+4 q)^2-(11 p q-4 q)^2=176 p q^2$

✓

Answer

$\begin{aligned} \text { LHS }= & (11 p q+4 q)^2-(11 p q-4 q)^2 \\ & =(11 p q+4 q+11 p q-4 q) \times(11 p q+4 q-11 p q+4 q) \\ & \text { [using Identity III] }\end{aligned}$
where $a=11 p q+4 q$ and $b=11 p q-4 q]$
$
\begin{array}{l}
=(22 p q)(8 q) \\
=176 p q^2=\text { RHS } \qquad Hence proved
\end{array}
$

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