Question

What is the 4th term in the binomial expansion ${(a+b)}^{10}$?

• A. $a^7{b}^3$
• B. $a^6{b}^4$
• C. $210a^6{b}^4$
• D. $120a^7{b}^3$
• E. $120a^3{b}^7$

Answer 1

The correct option is D $120a^7{b}^3$

Using the formula to find the $4^{th}$ term,
$T_{r+1}=n{C}_r{a}^{n-r}{b}^r$
$T_{3+1}=10C_3{a}^{10-3}{b}^3$
$T_4=10C_3{a}^7{b}^3$
$T_4=\frac{10!}{(10-3)!3!}{a}^7{b}^3$
$T_4=\frac{10\times 9\times 8\times 7!}{7!\times 3\times 2\times 1}{a}^7{b}^3$
$T_4=120a^7{b}^3$