select the correct answer.

what is the factored form of $1,458x^3 - 2$?

$2(9x - 1)(81x^2 + 9x + 1)$

$2(9x + 1)(81x^2 - 9x + 1)$

$(9x - 2)(81x^2 + 18x + 4)$

$(9x + 2)(81x^2 - 18x + 4)$

Question

select the correct answer.

what is the factored form of $1,458x^3 - 2$?

$2(9x - 1)(81x^2 + 9x + 1)$

$2(9x + 1)(81x^2 - 9x + 1)$

$(9x - 2)(81x^2 + 18x + 4)$

$(9x + 2)(81x^2 - 18x + 4)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Difference of Cubes", "Polynomial Factoring" ], "current_concepts": [ "Difference of Cubes", "Polynomial Factoring" ] } ## Factor out the greatest common factor $$ 1,458x^3 - 2 = 2(729x^3 - 1) $$ ## Apply the difference of cubes formula $$ \begin{aligned} a^3 - b^3 &= (a - b)(a^2 + ab + b^2) \ 729x^3 - 1 &= (9x)^3 - 1^3 \ &= (9x - 1)((9x)^2 + (9x)(1) + 1^2) \ &= (9x - 1)(81x^2 + 9x + 1) \end{aligned} $$ ## Combine the factored terms $$ 1,458x^3 - 2 = 2(9x - 1)(81x^2 + 9x + 1) $$

(A) $2(9x - 1)(81x^2 + 9x + 1)$

(B) $2(9x + 1)(81x^2 - 9x + 1)$

(C) $(9x - 2)(81x^2 + 18x + 4)$

(D) $(9x + 2)(81x^2 - 18x + 4)$

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

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Apply the difference of cubes formula

Combine the factored terms

Answer: