Suppose $a^m$ occurs in the (r + 1)th term in the expansion of $(1 + a)^{m + n}$. Now $T_{r+1}$ = $\,{}^{m+n}C_r (1)^{m+n-r} (a)^r$ = $\,{}^{m+n}C_r a^r$ On comparing power of a in $a^m$ and $T_{r + 1}$, we get r = m. Thus the coefficient of $a^m$ is ${}^{m+n}C_m$ = $\frac{(m+n)!}{m!(m+n-m)!}$ = $\frac{(m+n)!}{m!n!}$ ... (i) Suppose an occurs in the (r + 1)th term in the expansion of $(1 + a)^{m + n}$. On comparing power of a in $a^n$ and $T_{r + 1}$, we get, r = n Thus the coefficient of $a^n$ is $\,{}^{m+n}C_n$ = $\frac{(m+n)!}{n!(m+n-n)!}$ = $\frac{(m+n)!}{n!m!}$ ... (ii) From (i) & (ii) we proved that coefficient of am & an in expansion $(1 + a)^{m + n}$ are equal.