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Write the expanded form of (7a + 9b + 6c)2

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OSSC Excise SI (Mains) Official Paper (Held On: 17 Oct, 2024 Shift 1)
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  1. 49a² + 81b² + 36c² + 126ab + 108bc + 94ac
  2. 49a² + 81b² + 36c² + 130ab + 108bc + 84ac
  3. 49a² + 81b² + 36c² + 126ab + 103bc + 84ac
  4. 49a² + 81b² + 36c² + 126ab + 108bc + 84ac

Answer (Detailed Solution Below)

Option 4 : 49a² + 81b² + 36c² + 126ab + 108bc + 84ac

Detailed Solution

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Given:

Expression: (7a + 9b + 6c)2

Formula used:

(x + y + z)2 = x2 + y2 + z2 + 2xy + 2xz + 2yz

Calculation:

Let x = 7a, y = 9b, z = 6c

(7a + 9b + 6c)2 = (7a)2 + (9b)2 + (6c)2 + 2(7a)(9b) + 2(7a)(6c) + 2(9b)(6c)

⇒ (7a + 9b + 6c)2 = 49a2 + 81b2 + 36c2 + 126ab + 84ac + 108bc

Expanded form:

49a2 + 81b2 + 36c2 + 126ab + 84ac + 108bc

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