# How do you factor 81z^2 + 36z + 4?

May 20, 2015

Problem: Factor $81 {z}^{2} + 36 z + 4$.

This is an example of the square of the sum formula:

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

$a = 9 z$
$b = 2$

${\left(9 z\right)}^{2} + 2 \left(9 z\right) \left(2\right) + {2}^{2}$

The factorization of $81 {z}^{2} + 36 z + 4 = {\left(9 z + 2\right)}^{2}$.