Questions: 36y^2 + 12yz + z^2 =

Solution Steps

To factor the given quadratic expression completely, we can look for a pattern or use the quadratic formula. In this case, the expression resembles a perfect square trinomial. We can rewrite it as the square of a binomial.

1. Recognize the pattern of a perfect square trinomial.
2. Rewrite the expression as the square of a binomial.

We start with the expression: \[ 36y^{2} + 12yz + z^{2} \]

This expression can be recognized as a perfect square trinomial, which can be expressed in the form: \[ (a + b)^{2} = a^{2} + 2ab + b^{2} \] In our case, we can identify \(a = 6y\) and \(b = z\).

Using the identified values of \(a\) and \(b\), we can rewrite the expression as: \[ (6y + z)^{2} \]

Final Answer