Q. \((x-2)^3\)

We want to expand the expression \( (x-2)^3 \). This means we multiply \(x-2\) by itself three times.

Step 1: Rewrite the power as a product

\[
(x-2)^3 = (x-2)(x-2)(x-2).
\]

Step 2: Use the algebraic identity for a cube

There is a standard expansion formula:

\[
(a-b)^3 = a^3 – 3a^2b + 3ab^2 – b^3.
\]

Step 3: Match variables

In our problem, \(a=x\) and \(b=2\). Substitute into the formula:

\[
(x-2)^3 = x^3 – 3x^2(2) + 3x(2)^2 – (2)^3.
\]

Step 4: Simplify each term

Compute each part one at a time.

First term:

\[
x^3.
\]

Second term: \(-3x^2(2)\)

\[
-3x^2(2) = -6x^2.
\]

Third term: \(3x(2)^2\) and \((2)^2=4\)

\[
3x(2)^2 = 3x(4) = 12x.
\]

Fourth term: \(-(2)^3\) and \((2)^3=8\)

\[
-(2)^3 = -8.
\]

Step 5: Combine all simplified terms

\[
(x-2)^3 = x^3 – 6x^2 + 12x – 8.
\]

Final Answer

\[
\boxed{(x-2)^3 = x^3 – 6x^2 + 12x – 8.}
\]