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

Nov 29, 2017

$- {x}^{3} + 5 {x}^{2} - 7 x + 3$

#### Explanation:

$\text{expand the factors and collect like terms}$

${\left(x - 1\right)}^{2} = \left(x - 1\right) \left(x - 1\right) \leftarrow \textcolor{b l u e}{\text{expand using FOIL}}$

$\left(x - 1\right) \left(x - 1\right) = {x}^{2} - 2 x + 1$

$\text{now multiply expansion by factor } \left(3 - x\right)$

$\left(3 - x\right) \left({x}^{2} - 2 x + 1\right)$

$\text{multiply each term in the second factor by each term}$
$\text{in the first factor}$

$\textcolor{red}{3} \left({x}^{2} - 2 x + 1\right) \textcolor{red}{- x} \left({x}^{2} - 2 x + 1\right)$

$= 3 {x}^{2} - 6 x + 3 - {x}^{3} + 2 {x}^{2} - x \leftarrow \textcolor{b l u e}{\text{collect like terms}}$

$= - {x}^{3} + 5 {x}^{2} - 7 x + 3 \leftarrow \textcolor{red}{\text{in standard form}}$

$\text{to express a polynomial in "color(blue)"standard form}$

$\text{start with the term with the largest exponent of the variable}$
$\text{followed by terms of decreasing exponents in descending}$
$\text{order}$