# Question 22a38

Apr 12, 2017

${x}^{3} - 9 {x}^{2} + 26 x - 24$

#### Explanation:

To simplify this expression, or any expression, a good start would be putting the binomial before the polynomial. This will make it a lot easier to multiply. In this case, it is already this way.

Now we can begin to multiply.

Take the $\textcolor{b l u e}{\text{first term in the binomial}}$ and multiply it with $\textcolor{g r e e n}{\text{every term in the polynomial}}$.

Then take the $\textcolor{red}{\text{second term in the binomial}}$ and multiply it with $\textcolor{g r e e n}{\text{every term in the polynomial}}$.

$\left(x - 3\right) \left({x}^{2} - 6 x + 8\right)$

$\left(\textcolor{b l u e}{x} - 3\right) \left(\textcolor{g r e e n}{{x}^{2}} - 6 x + 8\right)$ $\textcolor{\mathmr{and} a n \ge}{\to} x \cdot {x}^{2} \textcolor{\mathmr{and} a n \ge}{\to} \textcolor{red}{{x}^{3}}$

 (color(blue)(x) - 3)(x^2   color(green)( - 6x) + 8)  $\textcolor{\mathmr{and} a n \ge}{\to} x \cdot - 6 x \textcolor{\mathmr{and} a n \ge}{\to} \textcolor{red}{- 6 {x}^{2}}$

 (color(blue)(x) - 3)(x^2 - 6x   color(green)( + 8))  $\textcolor{\mathmr{and} a n \ge}{\to} x \cdot 8 \textcolor{\mathmr{and} a n \ge}{\to} \textcolor{red}{8 x}$

 (x  color(red)( - 3))(color(green)(x^2) - 6x + 8)  $\textcolor{\mathmr{and} a n \ge}{\to} - 3 \cdot {x}^{2} \textcolor{\mathmr{and} a n \ge}{\to} \textcolor{red}{- 3 {x}^{2}}$

 (x  color(red)( - 3))(x^2   color(green)( - 6x) + 8)  $\textcolor{\mathmr{and} a n \ge}{\to} - 3 \cdot - 6 x \textcolor{\mathmr{and} a n \ge}{\to} \textcolor{red}{18 x}$

 (x  color(red)( - 3))(x^2 - 6x   color(green)( + 8)) # $\textcolor{\mathmr{and} a n \ge}{\to} - 3 \cdot 8 \textcolor{\mathmr{and} a n \ge}{\to} \textcolor{red}{- 24}$

Now all we have to do is add the terms that we got and simplify.

${x}^{3} + \left(- 6 {x}^{2}\right) + 8 x + \left(- 3 {x}^{2}\right) + 18 x + \left(- 24\right)$
${x}^{3} - 6 {x}^{2} + 8 x - 3 {x}^{2} + 18 x - 24$
${x}^{3} - 9 {x}^{2} + 26 x - 24$

As you can see, when we simplify our initial expression, we get our answer which is ${x}^{3} - 9 {x}^{2} + 26 x - 24$.