what is the factorization of (1,000x^6 - 27)?

$ (10x^2 - 3)(100x^2 + 30x^2 + 9) $
$ (10x^2 - 3)(100x^4 + 30x^2 + 9) $
$ (10x^3 - 3)(100x^2 + 30x^3 + 9) $
$ (10x^3 - 3)(100x^6 + 30x^3 + 9) $

Question

what is the factorization of (1,000x^6 - 27)?

$ (10x^2 - 3)(100x^2 + 30x^2 + 9) $
$ (10x^2 - 3)(100x^4 + 30x^2 + 9) $
$ (10x^3 - 3)(100x^2 + 30x^3 + 9) $
$ (10x^3 - 3)(100x^6 + 30x^3 + 9) $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Difference of Cubes", "Factoring Polynomials" ], "new_concepts": [], "current_concepts": [ "Difference of Cubes", "Factoring Polynomials" ] } ## Rewrite as a difference of cubes $$ 1,000x^6 - 27 = (10x^2)^3 - 3^3 $$ ## Apply the difference of cubes formula $$ a^3 - b^3 = (a - b)(a^2 + ab + b^2) $$ $$ \begin{aligned} a &= 10x^2 \ b &= 3 \end{aligned} $$ $$ (10x^2 - 3)((10x^2)^2 + (10x^2)(3) + 3^2) $$ ## Simplify the terms $$ (10x^2 - 3)(100x^4 + 30x^2 + 9) $$

(A) $(10x^2 - 3)(100x^2 + 30x^2 + 9)$

(B) $(10x^2 - 3)(100x^4 + 30x^2 + 9)$

(C) $(10x^3 - 3)(100x^2 + 30x^3 + 9)$

(D) $(10x^3 - 3)(100x^6 + 30x^3 + 9)$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Rewrite as a difference of cubes

Apply the difference of cubes formula

Simplify the terms

Answer: