Question

factor.
$u^2 - 12u + 36$

Explanation:

Step1: Identify the form

The quadratic \( u^2 - 12u + 36 \) is a perfect square trinomial. The form of a perfect square trinomial is \( a^2 - 2ab + b^2=(a - b)^2 \).

Step2: Match coefficients

Here, \( a = u \), \( 2ab = 12u \) (so \( 2b = 12 \) ⇒ \( b = 6 \)), and \( b^2 = 36 \) (which matches the constant term).

Step3: Apply the formula

Substitute \( a = u \) and \( b = 6 \) into \( (a - b)^2 \), we get \( (u - 6)^2 \).

Answer:

\( (u - 6)^2 \)