# How do you simplify (x-3)^2-4(x-3)+3?

Jun 17, 2018

#### Answer:

$\left(x - 6\right) \left(x - 4\right)$

#### Explanation:

Let $u = x - 3$

Hence, ${\left(x - 3\right)}^{2} - 4 \left(x - 3\right) + 3$ becomes ${u}^{2} - 4 u + 3$

Solving for u: (u^2-4u+3=(u-3)(u-1)
Therefore, subbing $u = x - 3$ back into the equation
$\left(x - 3 - 3\right) \left(x - 3 - 1\right) = \left(x - 6\right) \left(x - 4\right)$