Question

(x-1)^3-(x-1)^2+(x-1)

Answer 1

(x-1)*((x-1)^2 - (x-1)+1)
(x-1)*(x^2 - 2x + 1 - x + 1 + 1)
(x-1) * (x^2 - 3x + 3)

Ответ: (x-1) * (x^2 - 3x + 3

Answer 2

To simplify the expression (x-1)^3 - (x-1)^2 + (x-1), we can expand each term and then combine like terms.

Let's start by expanding each term:

(x-1)^3 = (x-1)(x-1)(x-1) = (x^2-2x+1)(x-1) = x^3-3x^2+3x-1

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

Now, let's substitute these expanded forms back into the original expression:

(x-1)^3 - (x-1)^2 + (x-1) = (x^3-3x^2+3x-1) - (x^2-2x+1) + (x-1)

Next, let's simplify by combining like terms:

= x^3 - 3x^2 + 3x - 1 - x^2 + 2x - 1 + x - 1

= x^3 - 4x^2 + 4x - 3

So, the simplified form of (x-1)^3 - (x-1)^2 + (x-1) is x^3 - 4x^2 + 4x - 3.