Pure Maths ( polynomials)Ask b, c only

Let +ve integers m, n , Σ(r=0 to mn)a_r*x^r=(1+x+x^2+....+x^m)^n------(*)
(a)(i)Σ(r=0 to mn)a_r=(m+1)^n
(ii)Σ(r=0 to mn)(-1)^r* a_r=2^n(m is odd) / 1(m is even)
(iii)Σ(r=0 to mn)2^r a_r=(2^(m+1)-1)^n
(b)By diff (*), show mnΣ(r=0 to mn)a_r=2Σ(r=1 to mn)r*a_r
(c)Show Σ(r=1 to m)r(-1)^r =m/2(m is even), -(m+1)/2 (m is odd)
Hence, show 2Σ(r=1 to mn)r a_r(-1)^r = mn(m is even), 0 (m is odd)