How do you factor the sum or difference of two cubes $x^3-27$ ?

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Answer 1 · 2015-04-09T06:08:28

The factor of $x^3-27=(x-3)(x^2+3x+9)$

Beginning Equation:

$x^3-27$

This is a case of factoring difference of cubes.

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

For $(x^3-27)$ :

$a^3=x^3$

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

$b^3=27$

$b=root(3)(27)=3$

$a=x, b=3$

$(x^3-27)=(x-3)(x^2+(x*3)+9)$ =

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

How do you factor the sum or difference of two cubes x^3-27x^3-27?