ANSWER
C. 240
EXPLANATION
We have to find the coefficient of the third term of (2x - 1)⁶. To do so, we have to find the expansion of this binomial, which is given by the Binomial Theorem Formula,
[tex](a+b)^n=\sum_{k=0}^n\binom{n}{k}a^{n-k}b^k[/tex]
In this case, n = 6, a = 2x, and b = -1. The third term is when k = 2 - note that k starts with 0, so the third term in this case is,
[tex]\binom{6}{2}(2x)^{6-2}(-1)^2=\frac{6!}{2!(6-2)!}\cdot(2x)^4\cdot1=\frac{6\cdot5\cdot4!}{2\cdot1\cdot4!}\cdot2^4x^4=\frac{6\cdot5}{2}\cdot16x^4=240x^4[/tex]
Hence, the coefficient of the third term is 240.
