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^6 A- ^6 A is equal to

Options

  1. A2 A (1- 1 2 ^2 2 A )
  2. B2 A (1- 3 4 ^2 2 A )
  3. C2 A (1+ 1 4 ^2 2 A )
  4. D2 A (1- 1 4 ^2 2 A )

Correct answer

D. 2 A (1- 1 4 ^2 2 A )

Step-by-step solution

The expression is ⁶ A - ⁶ A . Using the identity a³ - b³ = (a - b)(a² + ab + b²) , we let a = ² A and b = ² A . ⁶ A - ⁶ A = ( ² A - ² A)( ⁴ A + ² A ² A + ⁴ A) . Since ² A - ² A = 2A , the expression becomes 2A (( ² A + ² A)² - ² A ² A) . Substituting ² A + ² A = 1 , we get 2A (1 - ² A ² A) . Multiplying and dividing by 4, we have ² A ² A = 4 ² A ² A 4 = (2 A A)² 4 = ² 2A 4 . Therefore, the expression is 2A (1 - 1 4 ² 2A) . Answer: 2 A (1- 1 4 ^2 2 A )

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