Question

Third term in the expression $(x+a{)}^7$ is

• A. ${}^7{C}_2{x}^5{a}^2$
• B. ${}^7{C}_3{x}^4{a}^3$
• C. ${}^7{C}_4{x}^3{a}^4$
• D. ${}^7{C}_6{x}^1{a}^6$

Answer 1

The correct option is A ${}^7{C}_2{x}^5{a}^2$

Using pascal triangle, we get
$(x+a{)}^7={}^7{C}_0{x}^7+{}^7{C}_1{x}^{6}a+{}^7{C}_2{x}^5{a}^2+\cdots +{}^7{C}_7{a}^7$

$\therefore$ The third term is ${}^7{C}_2{x}^5{a}^2$