select the correct answer.

what is the factored form of $b^3 - 1,000$?

$(b + 10)(b^2 - 10b + 100)$

$(b - 10)(b^2 + 10b + 100)$

$(b - 10)(10b^2 + b + 100)$

$(b + 10)(10b^2 - b + 100)$

Question

select the correct answer.

what is the factored form of $b^3 - 1,000$?

$(b + 10)(b^2 - 10b + 100)$

$(b - 10)(b^2 + 10b + 100)$

$(b - 10)(10b^2 + b + 100)$

$(b + 10)(10b^2 - b + 100)$

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", "Polynomial Factoring" ], "new_concepts": [], "current_concepts": [ "Difference of Cubes", "Polynomial Factoring" ] } ## Identify the terms as perfect cubes $$ b^3 - 1,000 = b^3 - 10^3 $$ ## Apply the difference of cubes formula $$ x^3 - y^3 = (x - y)(x^2 + xy + y^2) $$ ## Substitute the values into the formula $$ \begin{aligned} x &= b \ y &= 10 \ b^3 - 10^3 &= (b - 10)(b^2 + 10b + 10^2) \ &= (b - 10)(b^2 + 10b + 100) \end{aligned} $$

(A) $(b + 10)(b^2 - 10b + 100)$

(B) $(b - 10)(b^2 + 10b + 100)$

(C) $(b - 10)(10b^2 + b + 100)$

(D) $(b + 10)(10b^2 - b + 100)$

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

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QUESTION IMAGE

Question

Explanation:

Identify the terms as perfect cubes

Apply the difference of cubes formula

Substitute the values into the formula

Answer: