# How do you factor x^2-4x+4 using the perfect squares formula?

${x}^{2} - 4 x + 4 = {\left(x - 2\right)}^{2}$

#### Explanation:

I think what is being referred to is the relationship:

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

We've been given the equation ${x}^{2} - 4 x + 4$ - let's factor using the above relationship.

We can take the ${x}^{2}$ term and therefore assign $x = a$. We can also see that the $+ 4$ can be assigned to the ${b}^{2}$ term, giving $b = \pm 2$.

Lastly, we can take the $- 4 x$ term, assign it to the $+ 2 a b$ and say:

$- 4 x = 2 a b$

$- 2 x = a b$

We can substitute $x$ in for $a$:

$- 2 x = x b$

$- 2 = b$

and this tells us we will use $b = - 2$ and not $b = 2$.

All in all, we'll get:

${x}^{2} - 4 x + 4 = {\left(x - 2\right)}^{2}$