Find the fourth term of the binomial expansion of ((x – k)^{5}) in descending powers of x.
-
A.
(10x^{3}k^{2}) -
B.
(5x^{3}k^{2}) -
C.
(-5x^{2}k^{3}) -
D.
(-10x^{2}k^{3})
Correct Answer: Option D
Explanation
((x – k)^{5} = ^{5}C_{0}x^{5}(-k)^{0} + ^{5}C_{1}x^{4}(-k)^{1} + …)
The fourth term in the expansion = (^{5}C_{4 – 1}(x)^{5 – 3}(-k)^{3 = 10 times x^{2} times -k^{3})
= (-10x^{2}k^{3})