What is the standard form of  y= (x-6)(x-4)(x-1)?

Jan 1, 2016

$y = {x}^{3} - 11 {x}^{2} + 34 x - 24$

Explanation:

To rewrite the equation in standard form, start by expanding the first two brackets:

y=(color(red)x color(green)(-6))(color(orange)x color(blue)(-4))(x-1)

y=(color(red)x(color(orange)x) $\textcolor{red}{+ x} \left(\textcolor{b l u e}{- 4}\right)$ $\textcolor{\mathmr{and} a n \ge}{+ x} \left(\textcolor{g r e e n}{- 6}\right)$ color(green)(-6)(color(blue)(-4)))(x-1)

Simplify.

$y = \left({x}^{2} - 4 x - 6 x + 24\right) \left(x - 1\right)$

$y = \left({x}^{2} - 10 x + 24\right) \left(x - 1\right)$

Expand the remaining two brackets:

y=(color(red)(x^2) $\textcolor{\mathmr{and} a n \ge}{- 10 x}$ color(blue)(+24))(color(green)x color(purple)(-1))

$y = \textcolor{red}{{x}^{2}} \left(\textcolor{g r e e n}{x}\right)$ $\textcolor{red}{+ {x}^{2}} \left(\textcolor{p u r p \le}{- 1}\right)$ $\textcolor{\mathmr{and} a n \ge}{- 10 x} \left(\textcolor{g r e e n}{x}\right)$ $\textcolor{\mathmr{and} a n \ge}{- 10 x} \left(\textcolor{p u r p \le}{- 1}\right)$ $\textcolor{b l u e}{+ 24} \left(\textcolor{g r e e n}{x}\right)$ $\textcolor{b l u e}{+ 24} \left(\textcolor{p u r p \le}{- 1}\right)$

Simplify.

$y = {x}^{3} - {x}^{2} - 10 {x}^{2} + 10 x + 24 x - 24$

$y = {x}^{3} - 11 {x}^{2} + 34 x - 24$