# What is the standard form of  y= (x-5)(x-2)+(3x-1)^2?

May 21, 2018

y=10x²-13x+11

See explanations below.

#### Explanation:

y=(x-5)(x-2) +(3x-1)²

The standard form of a polynomial is :
$y = {\sum}_{k = 0}^{n} {a}_{k} {x}^{k} = {a}_{0} + {a}_{1} x + \ldots + {a}_{n} {x}^{n}$, where ${a}_{k} \in \mathbb{R}$ and $k \in \mathbb{N}$.

In order to write it, you need to develop each term,
and to sum each term of same degree.

$y = \left(\textcolor{red}{x} - \textcolor{b l u e}{5}\right) \left(x - 2\right) + \left(\textcolor{g r e e n}{3 x} - \textcolor{p u r p \le}{1}\right) \cdot \left(3 x - 1\right)$

$y = \textcolor{red}{x \left(x - 2\right)} - \textcolor{b l u e}{5 \left(x - 2\right)} + \textcolor{g r e e n}{3 x \left(3 x - 1\right)} - \textcolor{p u r p \le}{\left(3 x - 1\right)}$

$y = \textcolor{red}{x \cdot x - 2 \cdot x} + \left(\textcolor{b l u e}{- 5 \cdot x - 5 \cdot \left(- 2\right)}\right) + \textcolor{g r e e n}{3 x \cdot 3 x - 3 x \cdot 1} - \textcolor{p u r p \le}{\left(3 x - 1\right)}$

y=color(red)(x²-2x)-color(blue)(5x+10)+color(green)(9x²-3x)-color(purple)(3x+1)

Finally, let's sum each term of same degree :

y=(color(red)(1)color(green)(+9))^(color(orange)(=10))x²+(color(red)(-2)color(blue)(-5)color(green)(-3)color(purple)(-3))^(color(orange)(=-13))x(color(blue)(+10)color(purple)(+1))^(color(orange)(=11))

y=10x²-13x+11