Question

fill in the blank with a number to make the expression a perfect square.
$u^2 + 6u + \square$

Explanation:

Step1: Recall perfect square formula

A perfect square trinomial has the form \(a^2 + 2ab + b^2=(a + b)^2\). For the given expression \(u^2+6u+\square\), we have \(a = u\) and \(2ab=6u\).

Step2: Solve for \(b\)

Substitute \(a = u\) into \(2ab = 6u\), we get \(2\times u\times b=6u\). Divide both sides by \(2u\) (assuming \(u
eq0\)), we have \(b=\frac{6u}{2u} = 3\).

Step3: Find the constant term

The constant term of the perfect square trinomial is \(b^2\). Since \(b = 3\), then \(b^2=3^2 = 9\). So the blank should be filled with 9.

Answer:

9