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)(n!)/(k!(n-k)!)a^(n-k)b^k`

Here n = 5, then

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

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

`(5!)/(3!(5-3)!)a^(5-3)b^3=(5!)/(3!\cdot2!)a^2b^3=10a^2b^3`

The 4th term will be

`10a^2b^3`

The correct answer is the letter C.