# What is the standard form of  y= (x-1)(2x-7)(3x-1)?

Nov 2, 2017

$6 {x}^{3} - 29 {x}^{2} + 30 x - 7$

#### Explanation:

To expand the polynomial we've been given, we'll need to repeatedly apply the distributive property as we go through each of the binomials. Since the bulk of the explanation here is calculation, I'll walk through and justify the steps here:

$\left(x - 1\right) \left(2 x - 7\right) \left(3 x - 1\right) =$
$= \setminus \left[\left(x - 1\right) 2 x - \left(x - 1\right) 7 \setminus\right] \left(3 x - 1\right)$ (distribute the binomial $x - 1$ to the $2 x$ and the $7$)
$= \left(2 {x}^{2} - 2 x - 7 x + 7\right) \left(3 x - 1\right)$ (distribute the $2 x$ and the $7$ to the $x$ and the $- 1$)
$= \left(2 {x}^{2} - 9 x + 7\right) \left(3 x - 1\right)$
$= \left(2 {x}^{2} - 9 x + 7\right) 3 x - \left(2 {x}^{2} - 9 x + 7\right)$ (distribute the trinomial $2 {x}^{2} - 9 x + 7$ to the $3 x$ and the $1$)
$= 2 {x}^{2} \left(3 x\right) - 9 x \left(3 x\right) + 7 \left(3 x\right) - 2 {x}^{2} + 9 x - 7$
$= 6 {x}^{3} - 27 {x}^{2} + 21 x - 2 {x}^{2} + 9 x - 7$
$= 6 {x}^{3} - 29 {x}^{2} + 30 x - 7$ (combine like terms)