I need to write a polynomial in SIMPLEST FORM having roots 2,-2 and 4. I have to gt rid of the parentheses by multiplying everything out.Did I do it correctly?

(x-2)(x+2)(x-4)original problem
1.x^2 + 2x-2x=x^2-4)
2. (x^2-4)(x-4)
3. x^3-4x^2-4x+16=0

the first step should be x^2+2x-2x-4 = x^2-4(I forgot to put the (-4)

So far, so good.

(x^2-4)(x-4) = x^3 - 4x^2 - 4x + 16

You don't need an equation, just the polynomial.

Is that in simplest form or am I suppose to do something else with it? It seems too easy-

To write a polynomial in simplest form given the roots, you need to start with the factored form of the polynomial and multiply it out. Let's go through the steps:

Given roots: 2, -2, and 4

1. Start with the factored form: (x - 2)(x + 2)(x - 4)
2. Multiply the first two factors using the distributive property: (x^2 - 4)(x - 4)
3. Apply the distributive property again to multiply the result from step 2 with the third factor: x^3 - 4x^2 - 4x + 16

So, the polynomial in simplest form with the given roots is, indeed, x^3 - 4x^2 - 4x + 16. Well done!