If ai(i=0,1,2,…,16) be real constants such that for every real value of x,1+x+x28=a0+a1x+a2x2+…+a16x16, then a5  is equal to:

1+x+x28=∑p,q,r≥0P+q+r=8 8!p!q!r!1pxqx2rFor a5, we require, q+2r=5⇒q=5,r=0,p=3 or q=3,r=1,p=4 or q=1,r=2,p=5Thus, coefficient of x5 is 8!5!3!+8!3!1!4!+8!1!2!5!=504.