Question

factor
$u^2 - 4u + 4$

Explanation:

Step1: Identify the form of the quadratic

The expression \( u^2 - 4u + 4 \) is a quadratic trinomial. We can check if it is a perfect square trinomial. A perfect square trinomial has the form \( a^2 - 2ab + b^2=(a - b)^2 \).
Here, \( a^2 = u^2 \), so \( a = u \); and \( b^2 = 4 \), so \( b = 2 \). Also, \( 2ab=2\times u\times2 = 4u \), which matches the middle term (with a negative sign, so it's \( - 2ab=-4u \)).

Step2: Apply the perfect square formula

Using the formula \( a^2 - 2ab + b^2=(a - b)^2 \), substituting \( a = u \) and \( b = 2 \), we get:
\( u^2-4u + 4=(u - 2)^2 \)

Answer:

\( (u - 2)^2 \)