_ x 0 ^3 x- ^3 x x^5 is equal to

Step-by-step solution

aligned & _ x 0 ^3 x- ^3 x x^5 & = _ x 0 [ array c (x+ x^3 3 + 2 15 x^5+ )^3 - (x- x^3 3 ! + x^5 5 ! + )^3 array ] x^5 & = _ x 0 [ array c (1+ x^2 2 + 2 15 x^4+ )^3 - (1- x^2 3 ! + x^4 5 ! + )^3 array ] x^2 & (1+ x^2 3 + 2 15 x^4+ )- (1- x^2 3 ! + x^4 5 ! + ) & = _ x 0 array c (1+ x^2 3 + )^2+ (1- x^2 3 ! + )^2 + (1+ x^2 3 + ) (1- x^2 3 ! + ) array x^2 & . [using (a^3-b^3 )=(a-b) (a^2+b^2+a b ) ] & = _ x 0 ( x^2 2 + x^4 8 + ) array c . (1+ x^2 3 + )^2+ (1- x^2 3 ! + )^2 + (1+ x^2 3 + ) (1- x^2 3 + ) array x^2 & = _