Question

select the correct answer.
what is the factored form of $x^3 + 216$
a. $(x - 6)(x^2 + 6x + 36)$
b. $(x + 6)(x^2 - 6x + 36)$
c. $(x + 6)(x^2 - 12x + 36)$
d. $(x + 6)(x^2 + 12x + 36)$

Explanation:

Step1: Identify sum of cubes

Recognize $x^3 + 216$ as $x^3 + 6^3$ (since $6^3=216$).

Step2: Apply sum of cubes formula

Use the sum of cubes identity: $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$.
Substitute $a=x$, $b=6$:
$$x^3 + 6^3 = (x+6)(x^2 - (x)(6) + 6^2)$$

Step3: Simplify the quadratic term

Calculate the terms in the quadratic factor:
$$(x+6)(x^2 - 6x + 36)$$

Answer:

B. $(x + 6)(x^2 - 6x + 36)$