Question

factor.
$u^2 + 18u + 81$

Explanation:

Step1: Recall perfect square formula

The perfect square trinomial formula is \(a^2 + 2ab + b^2=(a + b)^2\).

Step2: Identify \(a\) and \(b\) in the given expression

For the expression \(u^2+18u + 81\), we have \(a = u\) (since \(u^2=a^2\)), and \(2ab=18u\). Substituting \(a = u\) into \(2ab = 18u\), we get \(2\times u\times b=18u\), dividing both sides by \(2u\) (assuming \(u
eq0\)), we find \(b = 9\). Also, \(b^2=9^2 = 81\), which matches the constant term in the given expression.

Step3: Apply the perfect square formula

Using the formula \(a^2+2ab + b^2=(a + b)^2\) with \(a = u\) and \(b = 9\), we get \(u^2+18u + 81=(u + 9)^2\).

Answer:

\((u + 9)^2\)