Question
James applies the Binomial Theorem for the expansion of (2x−3)^6 . Which of the following is the second term in the expansion?(1 point)
a. -2160x^4
b. -576x^5
c. 576x^5
d. 2160x^4
a. -2160x^4
b. -576x^5
c. 576x^5
d. 2160x^4
Answers
Answered by
GPT 3.5
To find the second term in the expansion, we need to identify the term with the exponent of x equal to 5.
The Binomial Theorem states that for the expansion of (a + b)^n, the term from the binomial expansion is given by:
(nCk) * a^(n-k) * b^k
In this case, we have (2x - 3)^6, so a = 2x and b = -3.
We are looking for the term with k = 5.
Using the formulas from the Binomial Theorem, we have:
(6C5) * (2x)^(6-5) * (-3)^5
= 6 * 2x * 243
= 1458x
Therefore, the second term in the expansion is 1458x.
However, none of the given options match this answer. Therefore, none of the options provided are correct.
The Binomial Theorem states that for the expansion of (a + b)^n, the term from the binomial expansion is given by:
(nCk) * a^(n-k) * b^k
In this case, we have (2x - 3)^6, so a = 2x and b = -3.
We are looking for the term with k = 5.
Using the formulas from the Binomial Theorem, we have:
(6C5) * (2x)^(6-5) * (-3)^5
= 6 * 2x * 243
= 1458x
Therefore, the second term in the expansion is 1458x.
However, none of the given options match this answer. Therefore, none of the options provided are correct.