How do you factor the expression $3 x^{3} - 27 x$ $3x^3-27x$ ?

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Answer 1 · 2018-03-19T19:20:00

See a solution process below:

First, we can rewrite and factor as $x 3$ $x3$ out of this expression as:

$(3 x \cdot x^{2}) - (3 x \cdot 9) \Rightarrow$ $(3x * x^2) - (3x * 9) =>$

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

Now we can use this formula for the special case of this quadratic to complete the factoring:

$x^{2} - y^{2} = (x + y) (x - y)$ $color(red)(x)^2 - color(blue)(y)^2 = (color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y))$

$3 x (x^{2} - 9) \Rightarrow$ $3x(x^2 - 9) =>$

$3 x (x^{2} - 3^{2}) \Rightarrow$ $3x(color(red)(x)^2 - color(blue)(3)^2) =>$

$3 x (x + 3) (x - 3)$ $3x(color(red)(x) + color(blue)(3))(color(red)(x) - color(blue)(3))$

How do you factor the expression 3x^3-27x3x3−27x3x^3-27x?