解:(Ⅰ)二項式系數(shù)之和為2
n=256,可得n=8;…2分
設含x項為第r+1項,則T
r+1=


=

m
r
…3分
故

=1,即r=2,…4分
則

m
2=112,解得m=±2…6分
∵m∈R+,
∴m=2…7分
(Ⅱ)∵

展開式的通項為

•

,即


(其中r=0,1,2,…8;s=0,2,…6),…9分
令

,則3r+2s=12…10分
∴

或

或

…12分
∴x
2的系數(shù)為

(-1)
6+

2
2
(-1)
3+

=-1119…14分
分析:(Ⅰ)由二項式系數(shù)之和為2
n=256,可得n,再由二項展開式的通項公式結合含x項的系數(shù)為112可求的n的值;
(Ⅱ)由二項展開式的通項公式


可含求得x
2項的系數(shù).
點評:本題考查二項式定理的應用,著重考查二項展開式的通項公式的應用,注重轉化與方程思想的運用,屬于中檔題.