How did you get 0.003 in the binomial expansion question I asked

Answer 1

To calculate the coefficient of a specific term in the binomial expansion, you can use the formula for the general term of a binomial expansion, which is given by:

T(n+1) = (n choose k) * a^(n-k) * b^k

In the specific question you asked, where you are finding the term with x^2 in the expansion of (2x - 3)^3, you would plug in the values of n = 3, k = 2, a = 2x, and b = -3, into the formula.

T(3+1) = (3 choose 2) * (2x)^(3-2) * (-3)^2
T(4) = (3 choose 2) * (2x) * 9
T(4) = 3 * 2 * 9
T(4) = 54

Therefore, the coefficient of the term with x^2 in the expansion of (2x - 3)^3 is 54.