The correct option is A 6
We have,
(2√2x2+1+√2x2−1)⇒(2(√2x2+1−√2x2−1)(2x2+1)−(2x2−1))⇒(√2x2+1−√2x2−1)
So, the given expression can be written as
(√2x2+1+√2x2−1)6+(√2x2+1−√2x2−1)6
We know that
(a+b)6+(a−b)6=2[a6+6C2a4b2+6C4a2b4+b6]=2[a6+15a4b2+15a2b4+b6]
Putting a=√2x2+1,b=√2x2−1
(√2x2+1+√2x2−1)6+(√2x2+1−√2x2−1)6
=2[(2x2+1)3+15(2x2+1)2(2x2−1)+15(2x2+1)(2x2−1)2+(2x2−1)3]
So, the degree of the polynomial is 6.