factor $64 - x^{15}$.

$(4 - x^3)(16 + 4x^3 + x^3)$
$(4 - x^3)(16 + 4x^3 + x^6)$
$(4 - x^5)(16 + 4x^5 + x^5)$
$(4 - x^5)(16 + 4x^5 + x^{10})$

Question

factor $64 - x^{15}$.

$(4 - x^3)(16 + 4x^3 + x^3)$
$(4 - x^3)(16 + 4x^3 + x^6)$
$(4 - x^5)(16 + 4x^5 + x^5)$
$(4 - x^5)(16 + 4x^5 + x^{10})$

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": [], "current_concepts": [ "Difference of Cubes", "Factoring Polynomials" ] } ## Identify the terms as perfect cubes $$ \begin{aligned} 64 &= 4^3 \ x^{15} &= (x^5)^3 \end{aligned} $$ ## Apply the difference of cubes formula $$ \begin{aligned} a^3 - b^3 &= (a - b)(a^2 + ab + b^2) \ \text{Let } a = 4 &\text{ and } b = x^5 \end{aligned} $$ ## Substitute and simplify the expression $$ \begin{aligned} 64 - x^{15} &= (4 - x^5)(4^2 + 4(x^5) + (x^5)^2) \ &= (4 - x^5)(16 + 4x^5 + x^{10}) \end{aligned} $$

(A) $(4-x^3)(16+4x^3+x^3)$

(B) $(4-x^3)(16+4x^3+x^6)$

(C) $(4-x^5)(16+4x^5+x^5)$

(D) $(4-x^5)(16+4x^5+x^{10})$

{ "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 and simplify the expression

Answer: