# How do you factor completely z^2 + 36z + 324?

${z}^{2} + 36 z + 324 = {z}^{2} + 2 \left(18 z\right) + {18}^{2} = {\left(z + 18\right)}^{2}$
This is a perfect square trinomial: ${18}^{2} = 324$ and $36 = 2 \cdot 18$, so we find:
${z}^{2} + 36 z + 324 = {z}^{2} + 2 \left(18 z\right) + {18}^{2} = {\left(z + 18\right)}^{2}$