# How do you factor y=x^3-x^2-4x+4 ?

Dec 13, 2015

$y = \left(x - 2\right) \left(x + 2\right) \left(x - 1\right)$

#### Explanation:

Set the equation equal to zero

${x}^{3} - {x}^{2} - 4 x + 4 = y$

Group

$\left({x}^{3} - {x}^{2}\right) + \left(- 4 x + 4\right) = y$

Factor the greatest common from each group

$\implies {x}^{2} \left(x - 1\right) - 4 \left(x - 1\right) = y$

Factor out the greatest common factor from the expression

$\implies \left({x}^{2} - 4\right) \left(x - 1\right) = y$

Factor the difference of square (a^2-b^2 = (a-b)(a+b)

$\implies \left(x - 2\right) \left(x + 2\right) \left(x - 1\right) = y$