Show That: (4pq + 3q)2 − (4pq − 3q)2 = 48pq2

Show that: (4pq + 3q)² − (4pq − 3q)² = 48pq²

Answer in Brief

LHS

\[ = \left( 4pq + 3q \right)^2 - \left( 4pq - 3q \right)^2 \]

\[ = 4\left( 4pq \right)\left( 3q \right) \left[ \because \left( a + b \right)^2 - \left( a + b \right)^2 = 4ab \right]\]

\[ = 48p q^2 \]

= RHS

Because LHS is equal to RHS, the given equation is verified.

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