completely factor the expression, if possible.

\27x^3 + 8\

Question

completely factor the expression, if possible.

\27x^3 + 8\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Sum and Difference of Cubes" ], "new_concepts": [], "current_concepts": [ "Factoring Sum and Difference of Cubes" ] } ## Identify the structure of the expression Using the *Factoring Sum and Difference of Cubes* knowledge point $$ 27x^3 + 8 = (3x)^3 + 2^3 $$ ## Apply the sum of cubes formula Using the *Factoring Sum and Difference of Cubes* knowledge point $$ \begin{aligned} a^3 + b^3 &= (a + b)(a^2 - ab + b^2)\ (3x)^3 + 2^3 &= (3x + 2)((3x)^2 - (3x)(2) + 2^2)\ &= (3x + 2)(9x^2 - 6x + 4) \end{aligned} $$ $(3x + 2)(9x^2 - 6x + 4)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Sum and Difference of Cubes" ] }

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Question

Explanation:

Identify the structure of the expression

Apply the sum of cubes formula

Answer: