Simplify (5x − 2y)2 + (2x + 5y)2 + (5x + 2y)(5x − 2y).

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RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 2)
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  1. 55x2 − 25y2
  2. −55x2 + 25y2
  3. 54x2 + 25y2
  4. −54x2 − 25y2

Answer (Detailed Solution Below)

Option 3 : 54x2 + 25y2
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RRB NTPC Graduate Level Full Test - 01
100 Qs. 100 Marks 90 Mins

Detailed Solution

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Given:

Simplify (5x - 2y)2 + (2x + 5y)2 + (5x + 2y)(5x - 2y).

Formula used:

(a - b)2 = a2 - 2ab + b2

(a + b)2 = a2 + 2ab + b2

(a + b)(a - b) = a2 - b2

Calculation:

(5x - 2y)2 = 25x2 - 20xy + 4y2

(2x + 5y)2 = 4x2 + 20xy + 25y2

(5x + 2y)(5x - 2y) = 25x2 - 4y2

⇒ (5x - 2y)2 + (2x + 5y)2 + (5x + 2y)(5x - 2y)

⇒ (25x2 - 20xy + 4y2) + (4x2 + 20xy + 25y2) + (25x2 - 4y2)

⇒ 25x2 + 4x2 + 25x2 - 20xy + 20xy + 4y2 + 25y2 - 4y2

⇒ 54x2 + 25y2

∴ The correct answer is option (3).

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