current objective
recognize and use the appropriate method to

question

factor: $40ad^3 + 625a$.

provide your answer below:

Question

current objective
recognize and use the appropriate method to

question

factor: $40ad^3 + 625a$.

provide your answer below:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor Factoring", "Sum of Cubes" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor Factoring", "Sum of Cubes" ] } ## Factor out the greatest common factor Using the *Greatest Common Factor Factoring* knowledge point $$ \begin{aligned} \text{GCF}(40ad^3, 625a) &= 5a \ 40ad^3 + 625a &= 5a(8d^3 + 125) \end{aligned} $$ ## Apply the sum of cubes formula Using the *Sum of Cubes* knowledge point $$ \begin{aligned} 8d^3 + 125 &= (2d)^3 + 5^3 \ &= (2d + 5)((2d)^2 - (2d)(5) + 5^2) \ &= (2d + 5)(4d^2 - 10d + 25) \end{aligned} $$ ## Write the completely factored expression Using the *Greatest Common Factor Factoring* and *Sum of Cubes* knowledge points $$ 40ad^3 + 625a = 5a(2d + 5)(4d^2 - 10d + 25) $$ Factor: $40ad^3 + 625a$. Provide your answer below: $5a(2d + 5)(4d^2 - 10d + 25)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Apply the sum of cubes formula

Write the completely factored expression

Answer: