_ x 2 (1- x) (8 x^3- ^3 ) x ( -2 x)^4

Step-by-step solution

Let L = _ x 2 (1- x) (8 x^3- ^3 ) x ( -2 x)^4 = _ x 2 (1- x)(2 x- ) (4 x^2+ ^2+2 x ) x 16 ( 2 -x )^4 Let l₁= _ x 2 (4 x^2+ ^2+2 x )=3 ^2 and l₂= _ x 2 (1- x)(2 x- ) x 16 ( 2 -x )^4 aligned & Put 2 -x=h & x= 2 - h and as x 2 , ~h 0 & l₂= _ h 0 1- ( 2 -h )(-2 h) ( 2 -h ) 16 h^4 & =- 1 8 _ h 0 1- h^2 h h & =- 1 8 ( 1 2 ) 1 & = -1 16 & ~L =3 ^2 (- 1 16 )= -3 ^2 16 aligned