How do you factor $x^3-27v^3$ ?

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Answer 1 · 2016-04-10T00:19:49

$(x-3v)(x^2+3vx+9v^2)$

This problem is what is described as a Difference of Cubes

If we consider the equation:

$a^3-b^3$ where $a$ and $b$ are perfect cubes, we can factorise the problem using the formula:

$(a – b)(a^2 + ab + b^2)$

In your case, if we consider the equation:

$x^3−27v^3$

We notice that not only are the $x$ and $y$ terms cubes, but 27 is also a cube $(3^3=27)$ .

Therefore, if we substitute the values in to the Difference of Cubes formula, letting $x=a$ and $3v=b$ we get:

$(x-3v)(x^2+3vx+[3v]^2)$

Simplifying this we get the factored equation:

$(x-3v)(x^2+3vx+9v^2)$

How do you factor x^3-27v^3x^3-27v^3?