Writing as a simplified polynomial in standard form, what is the result when (x-4)^2 is subtracted from 9?

Answer 1

To find the result when (x-4)^2 is subtracted from 9, we just need to expand (x-4)^2 and then subtract it from 9.

(x-4)^2 is equal to (x-4)(x-4), so using the FOIL method, we have:
(x-4)(x-4) = x(x) + x(-4) - 4(x) - 4(-4) = x^2 - 4x - 4x + 16 = x^2 - 8x + 16

Now, we subtract this result from 9:
9 - (x^2 - 8x + 16) = 9 - x^2 + 8x - 16 = -x^2 + 8x - 7

Therefore, the simplified polynomial in standard form result of subtracting (x-4)^2 from 9 is -x^2 + 8x - 7.