" 12."(x)/(a^(4)+x^(4))

Prove that : Find the coefficient of x^(12)" in "(1+3x)/((1-4x)^(4)).

Find the GCD for each pair of the following polynomials 12(x^(4)-x^(3)), 8(x^(4)-3x^(3)+2x^(2)) whose LCM is 24^(3)(x-1)(x-2)

The LCM of the polynomials 12(x^(4)+x^(3)+x^(2)) and 18(x^(4)-x) is

If int (x^(8)-12x^(4)+4)/(x^(4)-4x^(2)+2)dx = x^(a)/a + (4x^(b))/b +2x+C , then the value of (a+b) is

Factorizing the difference of squares: (i)x^(8)-y^(8)(ii)a^(12)x^(4)-a^(4)x^(12)

Factorize each of the following algebraic expressions : x^(8)-y^(8)( ii) a^(12)x^(4)-a^(4)x^(12)

int(3x^(13)-+2x^(11))/((4x^(4)+3x^(2)+1)^(4))dx is equal to (A)(x^(12))/((4x^(4)+3x^(2)+1)^(4))+C(B)(2)/(3(4x^(4)+3x^(2)+1)^(3))+C(C)(x^(12))/(3(4x^(-4)+3x^(2)+1)^(4))(D)(x^(6))/(6(4x^(-4)+3x^(-2)+1)^(3))+C

The series expansion of log[(1 + x)^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]