Question

11．化簡：（1-x）⁵+（x+1）⁵．

Answer 1

分析 按照二項式定理把（1-x）⁵ 和（x+1）⁵ 分別展開，可得：（1-x）⁵+（x+1）⁵的結(jié)果．

解答 解：（1-x）⁵+（x+1）⁵ =${C}_{5}^{0}$-${C}_{5}^{1}$•x+${C}_{5}^{2}$•x²-${C}_{5}^{3}$•x³+${C}_{5}^{4}$•x⁴-${C}_{5}^{5}$•x⁵+${C}_{5}^{0}$+${C}_{5}^{1}$•x+${C}_{5}^{2}$•x²+${C}_{5}^{3}$•x³+${C}_{5}^{4}$•x⁴+${C}_{5}^{5}$x⁵
= ²${C}_{5}^{0}$+2${C}_{5}^{2}$•x²+2${C}_{5}^{4}$•x⁴=2+20x²+10x⁴．

點評 本題主要考查二項式定理的應(yīng)用，二項式展開式的通項公式，屬于基礎(chǔ)題．