If p + q = 3 and p - q = 1, find 2p² + 2q² - 4pq.
Show answer & explanation
Correct answer: A
Explanation
Given:
p + q = 3
p − q = 1
According to the formula:
(p − q)² = p² + q² − 2pq
(p − q)² = 1² = 1
⇒ p² + q² − 2pq = 1
Now,
2p² + 2q² − 4pq
= 2(p² + q² − 2pq)
= 2 × 1
= 2