Answer:
-36 is the coefficient of x^2 in the expansion of (2x - 3)^3.
Explanation:
Determining another way to write (2x - 3)^3:
- (2x - 3)^3 is the same as (2x - 3)(2x - 3)(2x - 3).
- Let's start by multiplying (2x - 3) and (2x - 3).
Then, we'll multiply this product by (2x - 3) to determine the coefficient of x^2 in the expansion of (2x - 3)^2:
Finding (2x - 3)(2x - 3):
(2x - 3)(2x - 3)
(2x * 2x) + (2x * -3) + (-3 * 2x) + (-3 * -3)
4x^2 - 6x - 6x + 9
4x^2 - 12x + 9
Finding (4x^2 - 12x + 9)(2x - 3):
Once we simplify, we can determine the coefficient of x^2:
(4x^2 - 12x + 9)(2x - 3)
(4x^2 * 2x) + (4x^2 * - 3) + (-12x * 2x) + (-12x * -3) + (9 * 2x) + (9 * -3)
8x^3 - 12x^2 - 24x^2 + 36x + 18x - 27
8x^3 - 36x^2 + 54x - 27
Thus, the coefficient of x^2 is -36.