Question

What is the value of the 4th term of the expansion (a + b)^5?A. 10a^3b^2B. A^5C. 10a^2b^3D. 5a^4b

Answer 1

Using the binomial, we have:

$(a+b)^n=\sum ^n_{k\mathop=0}\frac{n!}{k!(n-k)!}a^{n-k}b^k$

Here n = 5, then

$(a+b)^5=\sum ^5_{k\mathop{=}0}\frac{5!}{k!(5-k)!}a^{5-k}b^k$

The 4th term will be when k = 3, then

$\frac{5!}{3!(5-3)!}a^{5-3}b^3=\frac{5!}{3!\cdot2!}a^2b^3=10a^2b^3$

The 4th term will be

$10a^2b^3$

The correct answer is the letter C.