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Simplify the following.
(2x +3)2 − (x + 1)2.

This question was previously asked in
RRB NTPC Graduate Level CBT-I Official Paper (Held On: 05 Jun, 2025 Shift 2)
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  1. 4x2 + 12x + 8
  2.  4x2 + 10x + 6
  3.  3x2 + 7x + 6
  4. 3x2 + 10x + 8

Answer (Detailed Solution Below)

Option 4 : 3x2 + 10x + 8
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Detailed Solution

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Given:

(2x + 3)2 - (x + 1)2

Formula used:

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

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

Calculation:

(2x + 3)2 - (x + 1)2

⇒ [(2x)2 + 2 × 2x × 3 + 32] - [(x)2 + 2 × x × 1 + 12]

⇒ [4x2 + 12x + 9] - [x2 + 2x + 1]

⇒ 4x2 + 12x + 9 - x2 - 2x - 1

⇒ (4x2 - x2) + (12x - 2x) + (9 - 1)

⇒ 3x2 + 10x + 8

∴ The correct answer is option (4).

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