Q. \(x^{2}-4x+4\)

We are given the expression \(x^2 – 4x + 4\). The goal is typically to rewrite it in a simpler factored or completed-square form.

Step 1: Recognize a perfect square pattern

Notice that the first term is \(x^2\), and the last term is \(4\), which is \(2^2\). Also, the middle term is \(-4x\), which matches \(-2 \cdot x \cdot 2\). This suggests the expression is a perfect square of the form:

\[
x^2 – 4x + 4 = (x – 2)^2
\]

Step 2: Verify by expanding

Expand \((x – 2)^2\) to confirm it matches the original expression.

\[
(x – 2)^2 = (x – 2)(x – 2)
\]

Distribute each term:

\[
(x – 2)(x – 2) = x(x – 2) – 2(x – 2)
\]

Now distribute again:

\[
x(x – 2) = x^2 – 2x
\]
\[
-2(x – 2) = -2x + 4
\]

Add the results:

\[
x^2 – 2x – 2x + 4 = x^2 – 4x + 4
\]

Conclusion

Since the expansion matches the original expression, we conclude:

\[
x^2 – 4x + 4 = (x – 2)^2
\]