Final answer:
The expression equivalent to 9 - 15x in the form (3x - a)² - b is (3x - 5)² - 6. By equating the coefficient of x and the constant in the expansion, we can find the correct form, leading to answer option B.
Step-by-step explanation:
The expression 9 - 15x can be rewritten in the form (3x - a)² - b. To find which of the options provided is equivalent to 9 - 15x, we can expand each of the given options or use the process of elimination to determine the correct one.
Let's consider the term involving x in the given expression. Since we have -15x, and our (3x - a)² term implies that the coefficient of x in the binomial squared will be 9x², we can deduce that -15 must be equal to 2 times the product of 3 and the unknown 'a' in the equivalent expression. Hence, 'a' must be 5 because 2 * 3 * 5 = 30, and we have a negative sign before 15x suggesting that 'a' is positive.
Now check the constant term: the constant in our target expression is 9, which must be the result of (3*(-5))² minus 'b'. Since (3*(-5))² = 225, to get a constant of 9, 'b' must be 216.
However, none of the provided options include 'b' equal to 216. Upon closer evaluation, you can see that if we work from the option that has (3x - 5)², we end up with 9 - 15x when we expand it because (3x - 5)² = 9x² - 30x + 25. There is no need for a 'b' to get the term 9. Therefore, the correct answer is Option B, which is (3x - 5)² - 6.