Question

The total number of terms in the expansion of $(x+a{)}^{47}-(x-a{)}^{47}$ after simplification is

• A. $24$
• B. $47$
• C. $48$
• D. $96$

Answer 1

The correct option is A $24$

$(x+a{)}^{47}-(x-a{)}^{47}$
$={}^{47}{C}_0{x}^{47}{a}^0+{}^{47}{C}_1{x}^{46}{a}^1+{}^{47}{C}_2{x}^{45}{a}^2+....={}^{47}{C}_0{x}^{47}{a}^0-{}^{47}{C}_1{x}^{46}{a}^1+{}^{47}{C}_2{x}^{45}{a}^2-....=2({}^{47}{C}_0{x}^{47}{a}^0+{}^{47}{C}_2{x}^{45}{a}^2+....$
$24$ terms