Factor the expression: $$ x^{3} + 27 $$

Question

UpStudy AI · Accepted Answer

To factor the expression $$ x^{3} + 27 $$, recognize that it is a sum of cubes. The general formula for factoring a sum of cubes is:

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

Here, $$ a = x $$ and $$ b = 3 $$ since $$ 27 = 3^{3} $$. Applying the formula:

$$
x^{3} + 27 = x^{3} + 3^{3} = (x + 3)\left(x^{2} - x \cdot 3 + 3^{2}\right) = (x + 3)(x^{2} - 3x + 9)
$$

**Final Factored Form:**

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

Factor the expression: \( x^{3} + 27 \)