question 5 of 5

enter the correct answer in the box.

what is the factored form of this expression?

$64x^3 - 125$

write all factors in standard form.

Question

question 5 of 5

enter the correct answer in the box.

what is the factored form of this expression?

$64x^3 - 125$

write all factors in standard form.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Difference of Cubes" ], "new_concepts": [], "current_concepts": [ "Difference of Cubes", "Factoring Polynomials" ] } ## Identify the terms as perfect cubes $$ \begin{aligned} 64x^3 &= (4x)^3 \ 125 &= 5^3 \end{aligned} $$ ## Apply the difference of cubes formula $$ \begin{aligned} a^3 - b^3 &= (a - b)(a^2 + ab + b^2) \ a &= 4x, \quad b = 5 \end{aligned} $$ ## Substitute and simplify the factors $$ \begin{aligned} 64x^3 - 125 &= (4x - 5)((4x)^2 + (4x)(5) + 5^2) \ &= (4x - 5)(16x^2 + 20x + 25) \end{aligned} $$ What is the factored form of this expression? $64x^3 - 125$ Write all factors in standard form. $(4x - 5)(16x^2 + 20x + 25)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "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 factors

Answer: