x(x+a)(x+2a)(x+3a) =(x2+ax)(x2+5ax+6a2) =x4+ax3+5ax3+5a2x2+6a2x2+6a3x =x4+ax(x2+5x2+5ax+6ax+6a2) So, for terms to be perfect square, =(x+y)2(x+y)2=(x2+2xy+y2)(x2+y2+2xy) =x4+2x3y+x2y2+x2y2+2xy3+y4+2x3y+4x2y2+2xy3 =x4+xy(4x2+6xy+4y2)+y4 ...(ii) On comparing equations. (i) and (ii), as y=a a4 must be added to make it a perfect square. Let x=1 and a=1 solve 1(2)(3)(4)=24 1 need to complete square ∴ a4=14=1