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If p(x + y)2 = 5 and q(x - y)2 = 3 , then the simplified value of p2 (x + y)2 + 4pq xy – q2 (x - y)2 is :
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- – (p + q)
- 2 (p + q)
- p + q
- –2 (p + q)
- – (p + q)
Correct Option: B
p(x + y)2 = 5
| ⇒ (x + y)2 = | ||
| p |
| ⇒ q(x - y)2 = 3 ⇒ (x - y)2 = | ||
| q |
| ∴ (x + y)2 - (x - y)2 = | - | ||
| p | q |
| ⇒ 4xy = | - | = | |||
| p | q | pq |
| ∴ p2 (x + y)2 + 4pq xy – q2 (x - y)2 = p2 . | + pq. | - q2 . | |||
| p | pq | q |
p2 (x + y)2 + 4pq xy – q2 (x - y)2 = 5p + 5q – 3p – 3q = 2p + 2q
