 Hello and welcome to the session. I am Asha and I am going to help you solve the following problem that says find the value of a square plus root over a square minus 1 raise to the power 4 plus a square minus root over a square minus 1 raise to the power 4. So let us now begin with the solution and let a square is equal to x and root over a square minus 1 is equal to y. So the given expression can be written as x plus y raise to the power 4 plus x minus y raise to the power 4. Now expanding both these terms with the help of bi-normal theorem we have 4 c0 x raise to the power 4 into y raise to the power 0 plus 4 c1 x raise to the power 3 into y raise to the power 1 plus 4 c2 x square into y square plus 4 c3 x raise to the power 1 and y raise to the power 3 plus 4 c4 x raise to the power 0 and y raise to the power 4 plus now expanding the next bracket we have 4 c0 x raise to the power 4 into minus y raise to the power 0 plus 4 c1 x raise to the power 3 and minus y raise to the power 1 plus 4 c2 x raise to the power 2 minus y raise to the power 2 plus 4 c3 x raise to the power 1 and minus y raise to the power 3 plus 4 c4 x raise to the power 0 and minus y raise to the power 4. For the written as 4 c0 is 1 so x raise to the power 4 plus 4 x cube y plus 6 x square y square plus 4 x y cube plus y raise to the power 4 plus in the next bracket we have x raise to the power 4 minus 4 x cube y plus 6 x square y square minus 4 x y cube plus y raise to the power 4. So this one simplifying further and written as 2 x raise to the power 4 these two cancels out plus 12 x square y square again these two cancels out and we have plus 2 y raise to the power 4. Now on substituting a square y is equal to root over a square minus 1 and this expression we have the value of a square plus root over a square minus 1 raise to the power 4 plus a square minus root over a square minus 1 raise to the power 4 as 2 x is a square raise to the power 4 plus 12 x square into y square so a square whole square into y is root over a square minus 1 whole square plus 2 into y raise to the power 4 and y is root over a square minus one raised to the power four. So this is further equal to two a raised to the power eight plus twelve a raised to the power four into a square minus one plus two into a square minus one whole square which is further equal to two a raised to the power eight plus twelve a raised to the power six minus twelve a raised to the power four plus two times of a raised to the power four minus two a square plus one which is further equal to two a raised to the power eight plus twelve a raised to the power six minus twelve a raised to the power four plus two a raised to the power 4-4, a square plus 2 equal to 2 A raise to the power 8 plus 12 A raise to the power 6 minus 10 a raise to the power 4 minus 4 a square plus 2. Thus our answer is 2 A raise to the power 8 plus 12 A raise to the power 6 minus 10 to the power 4 minus 4 a square plus 2. So, this completes the session. Take care and have a good day.