Question

factor.
$u^2 + 4u + 4$

Explanation:

Step1: Identify the form

The quadratic \(u^2 + 4u + 4\) is a perfect square trinomial. The form of a perfect square trinomial is \(a^2 + 2ab + b^2=(a + b)^2\).

Step2: Match the terms

Here, \(a = u\) (since \(a^2=u^2\)), and \(2ab = 4u\). Substituting \(a = u\) into \(2ab = 4u\), we get \(2\times u\times b=4u\). Dividing both sides by \(2u\) (assuming \(u
eq0\)), we find \(b = 2\). Also, \(b^2=4\), which matches the constant term.

Step3: Apply the formula

Using the perfect square trinomial formula \(a^2 + 2ab + b^2=(a + b)^2\) with \(a = u\) and \(b = 2\), we have \(u^2 + 4u + 4=(u + 2)^2\).

Answer:

\((u + 2)^2\)