If p(x + y)² = 5 and q(x - y)² = 3, then the simplified value of p²(x + y)² + 4pqxy - q²(x - y)² is?

Solution(By Examveda Team)

$$\eqalign{ & p{\left( {x + y} \right)^2} = 5{\text{ and }}q{\left( {x - y} \right)^2} = 3 \cr & {\text{Put the value of }}x = 2{\text{ and }}y = 1 \cr & p{\left( {2 + 1} \right)^2} = 5 \cr & \Leftrightarrow p = \frac{5}{9} \cr & q{\left( {2 - 1} \right)^2} = 3 \cr & \Leftrightarrow q = 3 \cr & {p^2}{\left( {x + y} \right)^2} + 4pqxy - {q^2}{\left( {x - y} \right)^2} \cr} $$
  $$ = {\left( {\frac{5}{9}} \right)^2}{\left( {2 + 1} \right)^2} + 4 \times \frac{5}{9} \times 3 \times $$      $$2 \times $$ $$1 - $$ $${\left( 3 \right)^2}$$ $${\left( {2 - 1} \right)^2}$$
$$\eqalign{ & = \frac{{25}}{{81}} \times 9 + \frac{{40}}{3} - 9 \cr & = \frac{{25}}{9} + \frac{{40}}{3} - 9 \cr & = \frac{{25 + 120 - 81}}{9} \cr & = \frac{{64}}{9} \cr & {\text{Put the value of p and q in option (A)}} \cr & {\text{Option 1}} \to 2\left( {p + q} \right) \cr & = 2\left( {\frac{5}{9} + 3} \right) \cr & = 2 \times \frac{{32}}{9} \cr & = \frac{{64}}{9} \cr & {\text{Option A is satisfied}} \cr & {\text{So, }}2\left( {p + q} \right){\text{ is answer}} \cr} $$