If ai (i = 0, 1, 2, . . . 16)are 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!1pxqx2r
For , a5we require, q + 2r = 5
⇒ q=5,r=0,p=3or q=3,r=1,p=4
or q=1,r=2,p=5.
Thus, coefficient of x5 is
8!5!3!+8!3!1!4!+8!1!2!5!=504