# What is the standard form of  y= (x-5)(x-2)(x-1)?

Dec 18, 2017

$y = {x}^{3} - 8 {x}^{2} + 17 x - 10$

#### Explanation:

Note that:

$\left(x - \alpha\right) \left(x - \beta\right) \left(x - \gamma\right)$

$= {x}^{3} - \left(\alpha + \beta + \gamma\right) {x}^{2} + \left(\alpha \beta + \beta \gamma + \gamma \alpha\right) x - \alpha \beta \gamma$

So with $\alpha = 5$, $\beta = 2$ and $\gamma = 1$ we find:

$\left(x - 5\right) \left(x - 2\right) \left(x - 1\right) = {x}^{3} - 8 {x}^{2} + 17 x - 10$