# How do you factor 9z^2-12z+4?

##### 1 Answer
May 28, 2015

$9 {z}^{2} - 12 z + 4$

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like $a {z}^{2} + b z + c$, we need to think of 2 numbers such that:
${N}_{1} \cdot {N}_{2} = a \cdot c = 9 \cdot 4 = 36$
and
${N}_{1} + {N}_{2} = b = - 12$
After trying out a few numbers we get ${N}_{1} = - 6$ and ${N}_{2} = - 6$
$- 6 \cdot \left(- 6\right) = 36$, and $\left(- 6\right) + \left(- 6\right) = - 12$

$9 {z}^{2} - 12 z + 4 = 9 {z}^{2} - 6 z - 6 z + 4$

$= 3 z \left(3 z - 2\right) - 2 \left(3 z - 2\right)$
=color(green)((3z-2)(3z-2)

note : We know that $\textcolor{g r e e n}{{\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}}$