write the general form of

f(x)=4(x-1)^-8
(x-1) (x-1)=
4(x^-2x+1)-8
4x^-2x-8

Use a number with exponents.

4(x-1)^2 - 8
4(x^2-2x+1)-8
4x^2-8x+4-8
4x^2-8x-4

You must multiply the 4 by each term in the parentheses, not just the first one.

4(2+6) = 4*2 + 4*6 = 8+24 = 32
NOT
4(2+6) = 4*2+6 = 8+6 = 14

after all, 2+6=8, and 4*8 = 32

f(x) = 4(x-1)^2 - 8

= 4(x^2 - 2x + 1) - 8
= 4x^2 - 8x + 4 - 8
= 4x^2 - 8x - 4

To write the general form of the function f(x) = 4(x-1)^-8, we need to simplify the expression.

First, let's expand the exponent using the power rule.

Recall that (a^m)^n = a^(m*n).
In this case, (x-1)^-8 can be written as (1/(x-1))^8.

Next, we can distribute the exponent to each term within the parentheses:
(1^8) / (x^8 - 8x^7 + 28x^6 - 56x^5 + 70x^4 - 56x^3 + 28x^2 - 8x + 1)

Now, we can simplify this expression by collecting like terms and combining them. Based on the above expression, the general form of the function f(x) is:

f(x) = 1/(x^8 - 8x^7 + 28x^6 - 56x^5 + 70x^4 - 56x^3 + 28x^2 - 8x + 1)

Therefore, the general form of the function is f(x) = 1/(x^8 - 8x^7 + 28x^6 - 56x^5 + 70x^4 - 56x^3 + 28x^2 - 8x + 1).