what is $64x^6 + 27$ written as a sum of cubes?

$(4x)^3 + 3^3$
$(4x^2)^3 + 3^3$
$(4x^2)^3 + 9^3$
$(4x^3)^3 + 3^3$

Question

what is $64x^6 + 27$ written as a sum of cubes?

$(4x)^3 + 3^3$
$(4x^2)^3 + 3^3$
$(4x^2)^3 + 9^3$
$(4x^3)^3 + 3^3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Sum of Cubes", "Perfect Cubes", "Cube Root of Monomials" ], "new_concepts": [], "current_concepts": [ "Sum of Cubes", "Perfect Cubes", "Cube Root of Monomials" ] } ## Rewrite the first term as a perfect cube Using the *Cube Root of Monomials* and *Perfect Cubes* knowledge points $$ \begin{aligned} &64x^6 = (4)^3 \cdot (x^2)^3 = (4x^2)^3 \end{aligned} $$ ## Rewrite the second term as a perfect cube Using the *Perfect Cubes* knowledge point $$ \begin{aligned} &27 = 3^3 \end{aligned} $$ ## Express the polynomial as a sum of cubes Using the *Sum of Cubes* knowledge point $$ \begin{aligned} &64x^6 + 27 = (4x^2)^3 + 3^3 \end{aligned} $$

(A) $(4x)^3 + 3^3$

(B) $(4x^2)^3 + 3^3$

(C) $(4x^2)^3 + 9^3$

(D) $(4x^3)^3 + 3^3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Sum of Cubes" ] }

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QUESTION IMAGE

Question

Explanation:

Rewrite the first term as a perfect cube

Rewrite the second term as a perfect cube

Express the polynomial as a sum of cubes

Answer: