Question

X^2(x-2)-18x(x-2)+81(x-2)

Answer 1

(x-2)(x^2-18x+81)=(x-2)(x-9)^2

Answer 2

Ответ:

(x-2)(x-9)²

Объяснение:

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Answer 3

To simplify the expression $x^2(x-2) - 18x(x-2) + 81(x-2)$, you can factor out the common factor $(x-2)$ from each term:

$$\begin{align*} x^2(x-2) - 18x(x-2) + 81(x-2) &= (x-2)(x^2 - 18x + 81) \end{align*}$$

Now, you can simplify the expression $x^2 - 18x + 81$ by recognizing it as a perfect square trinomial. It factors as:

$$\begin{align*} x^2 - 18x + 81 &= (x - 9)(x - 9) \\ &= (x - 9)^2 \end{align*}$$

So, your simplified expression is:

$$\begin{align*} (x-2)(x-9)^2 \end{align*}$$

This is the factored form of the given expression.