Question

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

Explanation:

Step1: Recall the perfect square formula

The perfect square trinomial formula is \((a + b)^2 = a^2 + 2ab + b^2\). In the given expression \(v^2 + 2v + \square\), we can see that \(a = v\) (since \(a^2 = v^2\)) and \(2ab = 2v\).

Step2: Solve for \(b\)

We know that \(2ab = 2v\) and \(a = v\). Substituting \(a = v\) into \(2ab = 2v\), we get \(2\times v\times b = 2v\). Dividing both sides by \(2v\) (assuming \(v
eq0\)), we find that \(b = 1\).

Step3: Find the value of \(b^2\)

Since the third term of the perfect square trinomial is \(b^2\), and we found that \(b = 1\), then \(b^2 = 1^2 = 1\). So the number to fill in the blank is \(1\).

Answer:

\(1\)