completely factor the given polynomial, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\27 - 64y^3\

Question

completely factor the given polynomial, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\27 - 64y^3\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Difference of Cubes", "Factoring Sum and Difference of Cubes" ], "new_concepts": [], "current_concepts": [ "Difference of Cubes", "Factoring Sum and Difference of Cubes" ] } ## Identify the structure of the expression Using the *Difference of Cubes* knowledge point $$ 27 - 64y^3 = 3^3 - (4y)^3 $$ ## Apply the factoring formula Using the *Factoring Sum and Difference of Cubes* knowledge point $$ \begin{aligned} a^3 - b^3 &= (a - b)(a^2 + ab + b^2)\ 27 - 64y^3 &= (3 - 4y)(3^2 + 3(4y) + (4y)^2)\ &= (3 - 4y)(9 + 12y + 16y^2) \end{aligned} $$ $(3 - 4y)(9 + 12y + 16y^2)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Sum and Difference of Cubes" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the structure of the expression

Apply the factoring formula

Answer: