completely factor the expression, if possible.

\8y^6 + 27\

Question

completely factor the expression, if possible.

\8y^6 + 27\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "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 $$ 8y^6 + 27 = (2y^2)^3 + 3^3 $$ ## Apply the sum of cubes formula Using the *Factoring Sum and Difference of Cubes* knowledge point $$ \begin{aligned} a &= 2y^2 \ b &= 3 \ a^3 + b^3 &= (a + b)(a^2 - ab + b^2) \ 8y^6 + 27 &= (2y^2 + 3)((2y^2)^2 - (2y^2)(3) + 3^2) \ &= (2y^2 + 3)(4y^4 - 6y^2 + 9) \end{aligned} $$ Completely factor the expression, if possible. $8y^6 + 27 =$ $(2y^2 + 3)(4y^4 - 6y^2 + 9)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "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: