Question

factorise x^4/4+4/x^4+1, by a^2-b^2.

Answer 1

Hope it will help you.

Answer 2

x⁴/4  + 4/x⁴  + 1 =  (x²/2   +  2/x² + 1)(x²/2   +  2/x² - 1)

Step-by-step explanation:

x⁴/4  + 4/x⁴  + 1

= (x²/2)²  + (2/x²)²   +  1

= (x²/2)²  + (2/x²)²   + 2 - 1

= (x²/2)²  + (2/x²)²   + 2(x²/2)(2/x²) - 1

Using (a + b)² = a² + b² + 2ab

a = x²/2  b = 2/x²

= (x²/2   +  2/x²)²  - 1

=  (x²/2   +  2/x²)²  - 1²

Using a² - b² = (a + b)(a - b)

a = x²/2   +  2/x²  

b = 1

=  (x²/2   +  2/x² + 1)(x²/2   +  2/x² - 1)

x⁴/4  + 4/x⁴  + 1 =  (x²/2   +  2/x² + 1)(x²/2   +  2/x² - 1)

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