Find the 3rd term of ((frac{x}{2} – 1)^{8}) in descending order of x.
-
A.
(frac{x^{7}}{8}) -
B.
(frac{7x^{6}}{16}) -
C.
(frac{7x^{5}}{4}) -
D.
(frac{35x^{4}}{8})
Correct Answer: Option B
Explanation
((frac{x}{2} – 1)^{8} = ^{8}C_{8}(frac{x}{2})^{8}(-1)^{0} + ^{8}C_{7}(frac{x}{2})^{7}(-1)^{1} + ^{8}C_{6}(frac{x}{2})^{6}(-1)^{2} + …)
(text{The third term in the expansion =} ^{8}C_{6}(frac{x}{2})^{6}(-1)^{2})
= (frac{8!}{6!2!}(frac{x^{6}}{64})(1) )
= (28 times frac{x^{6}}{64} = frac{7x^{6}}{16})