The factor of the expression is \((x-3)\left(x^{2}+3 x+9\right)$\).
Factors
Given:
\(x^{3}-27$\)
Rewrite 27 as \($3^{3}$\)
then, we get \(x^{3}-3^{3}$\)
Since both terms are perfect cubes, factor using the difference of cubes formula, we get
\($a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)$\)
where a = x and b
\(&(x-3)\left(x^{2}+x \cdot 3+3^{2}\right)\)
Simplifying the given equation as,
Move 3 to the left of x.
\((x-3)\left(x^{2}+3 x+3^{2}\right)$\)
Raise 3 to the power of 2.
\((x-3)\left(x^{2}+3 x+9\right)$\)
Therefore, the factor of the expression is
\((x-3)\left(x^{2}+3 x+9\right)$\).
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