If 2p + 5q = 12 and pq = 3, find the value of 4p2 + 25 q2.

If 2p + 5q = 12

pq = 3

Find the value of 4p² + 25 q²

( a + b )² = a² + b² + 2ab

2p + 5q = 12

Squaring on both sides,

4p² + 25p² + 2 × 2p × 5q = 144

4p² + 25p² + 20pq = 144

4p² + 25p² = 144 - 20pq

4p² + 25p² = 144 - 20 × 3

4p² + 25p² = 84