Question #22a38

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Question #22a38

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Answer 1 · 2017-04-12T00:34:29

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

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 $first term in the binomial$ $color(blue)"first term in the binomial"$ and multiply it with $every term in the polynomial$ $color(green)"every term in the polynomial"$ .

Then take the $second term in the binomial$ $color(red)"second term in the binomial"$ and multiply it with $every term in the polynomial$ $color(green)"every term in the polynomial"$ .

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

$(x - 3) (x^{2} - 6 x + 8)$ $(color(blue)(x) - 3)(color(green)(x^2) - 6x + 8)$ $\to x \cdot x^{2} \to x^{3}$ $color(orange)(->) x * x^2 color(orange)(->) color(red)(x^3)$

$(x - 3) (x^{2}$ $(color(blue)(x) - 3)(x^2$ $- 6 x + 8)$ $color(green)( - 6x) + 8)$ $\to x \cdot - 6 x \to - 6 x^{2}$ $color(orange)(->) x * -6x color(orange)(->) color(red)(-6x^2)$

$(x - 3) (x^{2} - 6 x$ $(color(blue)(x) - 3)(x^2 - 6x$ $+ 8)$ $color(green)( + 8))$ $\to x \cdot 8 \to 8 x$ $color(orange)(->) x * 8 color(orange)(->) color(red)(8x)$

$(x$ $(x$ $- 3) (x^{2} - 6 x + 8)$ $color(red)( - 3))(color(green)(x^2) - 6x + 8)$ $\to - 3 \cdot x^{2} \to - 3 x^{2}$ $color(orange)(->) -3 * x^2 color(orange)(->) color(red)(-3x^2)$

$(x$ $(x$ $- 3) (x^{2}$ $color(red)( - 3))(x^2$ $- 6 x + 8)$ $color(green)( - 6x) + 8)$ $\to - 3 \cdot - 6 x \to 18 x$ $color(orange)(->) -3 * -6x color(orange)(->) color(red)(18x)$

$(x$ $(x$ $- 3) (x^{2} - 6 x$ $color(red)( - 3))(x^2 - 6x$ $+ 8)$ $color(green)( + 8))$ $\to - 3 \cdot 8 \to - 24$ $color(orange)(->) -3 * 8 color(orange)(->) color(red)(-24)$

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

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

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

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Question #22a38

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