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Factors of (16 - x6 + 2x3 y3 - y6) are -

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Rajasthan 3rd Grade (Maths & Science) Official Paper (Held On: 25 Feb 2023 Shift 2)
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  1. (x3 - y3 + 4) (x3 + y3 + 4)
  2. (x3 + y3 + 4) (x3 + y3​ - 4)
  3. (x3 - y3 + 4) (y3 - x3​ + 4)
  4. (x3 - y3 + 4) (x3 - y3​ - 4)

Answer (Detailed Solution Below)

Option 3 : (x3 - y3 + 4) (y3 - x3​ + 4)
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Detailed Solution

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Solution

⇒ 16 - x6 + 2x3 y3 - y6

⇒ 16 - (x6 - 2x3 y3 + y6)  ...(a + b)2 = a2 + b2 + 2ab

⇒ 16 - (x3 -  y3)2

⇒ 42 - (x3 -  y3)2        ...(a2 - b2) = (a+b) × (a-b)

⇒ (x3 - y3 + 4) (y3 - x3 + 4) 

The correct option is 3.

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