Question

select the correct answer.

what is the factored form of \\(x^3 + 216\\)?

\\((x - 6)(x^2 + 6x + 36)\\)
\\((x + 6)(x^2 - 6x + 36)\\)
\\((x + 6)(x^2 - 12x + 36)\\)
\\((x + 6)(x^2 + 12x + 36)\\)

Explanation:

Identify the sum of cubes structure

$$ x^3 + 216 = x^3 + 6^3 $$

Apply the sum of cubes formula

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

$$ x^3 + 6^3 = (x + 6)(x^2 - 6x + 6^2) $$

Simplify the expression

$$ x^3 + 216 = (x + 6)(x^2 - 6x + 36) $$

Answer:

• (A) \((x - 6)(x^2 + 6x + 36)\)
• (B) \((x + 6)(x^2 - 6x + 36)\) (Correct answer)
• (C) \((x + 6)(x^2 - 12x + 36)\)
• (D) \((x + 6)(x^2 + 12x + 36)\)