How do you simplify $x^3+3$ ?

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Answer 1 · 2016-04-30T11:01:17

$x^3+3=(x+root(3)(3))(x^2-root(3)(3)x+root(3)(9))$

This is already in simplest form unless you count factorisation.

We can treat this expression as a sum of cubes and use the sum of cubes identity:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

with $a=x$ and $b=root(3)(3)$ as follows:

$x^3+3$

$=x^3+(root(3)(3))^3$

$=(x+root(3)(3))(x^2-x(root(3)(3))+(root(3)(3))^2)$

$=(x+root(3)(3))(x^2-root(3)(3)x+root(3)(9))$

How do you simplify x^3+3x^3+3 ?