Question

factor completely. \\( r^2 + 2r + 1 \\)

Explanation:

Step1: Recall perfect square formula

The perfect square trinomial formula is \(a^2 + 2ab + b^2=(a + b)^2\). For the expression \(r^2+2r + 1\), we can identify \(a = r\) and \(b = 1\) since \(a^2=r^2\), \(2ab = 2\times r\times1=2r\) and \(b^2 = 1^2 = 1\).

Step2: Apply the formula

Using the perfect square trinomial formula \(a^2+2ab + b^2=(a + b)^2\) with \(a=r\) and \(b = 1\), we get \(r^2+2r + 1=(r + 1)^2\).

Answer:

\((r + 1)^2\)