How do you simplify $(x + 3) (x^{2} - 4 x + 9)$ $(x + 3)(x^2 - 4x + 9)$ ?

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How do you simplify $(x + 3) (x^{2} - 4 x + 9)$ $(x + 3)(x^2 - 4x + 9)$ ?

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Answer 1 · 2017-04-12T00:58:20

$x^{3} - x^{2} - 3 x + 27$ $x^3 - x^2 - 3x + 27$

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 $every term in the polynomial$ $color(green)"every term in the polynomial"$ .

$(x + 3) (x^{2} - 4 x + 9)$ $(x + 3)(x^2 - 4x + 9)$

$(x + 3) (x^{2} - 4 x + 9)$ $(color(blue)(x) + 3)(color(green)(x^2) - 4x + 9)$ $\to x \cdot x^{2} \to x^{3}$ $color(orange)(->) x * x^2 color(orange)(->) color(red)(x^3)$

$(x + 3) (x^{2}$ $(color(blue)(x) + 3)(x^2$ $- 4 x + 9)$ $color(green)( - 4x) + 9)$ $\to x \cdot - 4 x \to - 4 x^{2}$ $color(orange)(->) x * -4x color(orange)(->) color(red)(-4x^2)$

$(x + 3) (x^{2} - 4 x$ $(color(blue)(x) + 3)(x^2 - 4x$ $+ 9)$ $color(green)( + 9))$ $\to x \cdot 9 \to 9 x$ $color(orange)(->) x * 9 color(orange)(->) color(red)(9x)$

$(x$ $(x$ $+ 3) (x^{2} - 4 x + 9)$ $color(red)( + 3))(color(green)(x^2) - 4x + 9)$ $\to 3 \cdot x^{2} \to 3 x^{2}$ $color(orange)(->) 3 * x^2 color(orange)(->) color(red)(3x^2)$

$(x$ $(x$ $+ 3) (x^{2}$ $color(red)( + 3))(x^2$ $- 4 x + 9)$ $color(green)( - 4x) + 9)$ $\to 3 \cdot - 4 x \to - 12 x$ $color(orange)(->) 3 * -4x color(orange)(->) color(red)(-12x)$

$(x$ $(x$ $+ 3) (x^{2} - 4 x$ $color(red)( + 3))(x^2 - 4x$ $+ 9)$ $color(green)( + 9))$ $\to 3 \cdot 9 \to 27$ $color(orange)(->) 3 * 9 color(orange)(->) color(red)(27)$

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

$x^{3} + (- 4 x^{2}) + 9 x + 3 x^{2} + (- 12 x) + 27$ $x^3 + (-4x^2) + 9x + 3x^2 + (-12x) + 27$
$x^{3} - 4 x^{2} + 9 x + 3 x^{2} - 12 x + 27$ $x^3 - 4x^2 + 9x + 3x^2 - 12x + 27$
$x^{3} - x^{2} - 3 x + 27$ $x^3 - x^2 - 3x + 27$

As you can see, when we simplify our initial expression, we get our answer which is $x^{3} - x^{2} - 3 x + 27$ $x^3 - x^2 - 3x + 27$ .

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How do you simplify $(x + 3) (x^{2} - 4 x + 9)$ $(x + 3)(x^2 - 4x + 9)$ ?

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How do you simplify (x + 3)(x^2 - 4x + 9)(x+3)(x2−4x+9)(x + 3)(x^2 - 4x + 9)?

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How do you simplify $(x + 3) (x^{2} - 4 x + 9)$ $(x + 3)(x^2 - 4x + 9)$ ?