Question

factor.
$9u^2 + 24u + 16$

Explanation:

Step1: Identify the form of the quadratic

The quadratic \(9u^2 + 24u + 16\) is a perfect square trinomial. A perfect square trinomial has the form \(a^2 + 2ab + b^2=(a + b)^2\). Here, \(9u^2=(3u)^2\) and \(16 = 4^2\), and \(2ab=2\times3u\times4 = 24u\), which matches the middle term.

Step2: Apply the perfect square trinomial formula

Using the formula \(a^2+2ab + b^2=(a + b)^2\) with \(a = 3u\) and \(b = 4\), we get \((3u + 4)^2\).

Answer:

\((3u + 4)^2\)