Question

(8x^2 - 15x) - (x^2 - 27x) = ax^2 + bx. If the equation above is true for all values of x, what is the value of b - a?

A) b - a = -11
B) b - a = -12
C) b - a = -13
D) b - a = -14

Answer 1

The value of b - a is obtained by simplifying the given equation and comparing coefficients, resulting in a value of 5, which is not listed in the provided options.

Step-by-step explanation:

To solve the problem, we need to simplify the left side of the equation (8x^2 - 15x) - (x^2 - 27x) and compare it to the right side of the equation ax^2 + bx. So let's do that step by step:

1. Distribute the negative sign to terms within the second parentheses: 8x^2 - 15x - x^2 + 27x.
2. Combine like terms: (8x^2 - x^2) + (-15x + 27x) results in 7x^2 + 12x.

Now we can see that 7x^2 + 12x is the same as ax^2 + bx, which means a = 7 and b = 12.

To find the value of b - a, we subtract a from b: 12 - 7 = 5.

Therefore, none of the options A) b - a = -11, B) b - a = -12, C) b - a = -13, or D) b - a = -14 are correct. The value of b - a is actually 5.