Find the third term in the expansion of ((a – b)^{6}) in ascending powers of b.
-
A.
(-15a^{4}b^{2}) -
B.
(15a^{4}b^{2}) -
C.
(-15a^{3}b^{3}) -
D.
(15a^{3}b^{3})
Correct Answer: Option B
Explanation
((a – b)^{6} = ^{6}C_{0}(a)^{6}(-b)^{0} + ^{6}C_{1}(a)^{5}(-b)^{1} + ^{6}C_{2}(a)^{4}(-b)^{2} + …)
Third term = (^{6}C_{2}(a)^{4}(-b)^{2} = frac{6!}{(6-2)! 2!}(a^4)(b^2))
= (15a^{4}b^{2})