what is the fully factored form of (81x^2 - 576)?

- ((9x - 24)(9x + 24))
- (9(3x + 8)(3x - 8))
- none of these
- (3(3x - 8)^2)

Question

what is the fully factored form of (81x^2 - 576)?

- ((9x - 24)(9x + 24))
- (9(3x + 8)(3x - 8))
- none of these
- (3(3x - 8)^2)

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": [ "Greatest Common Factor", "Difference of Squares" ], "current_concepts": [ "Greatest Common Factor", "Difference of Squares", "Polynomial Factoring" ] } ## Factor out the greatest common factor $$ \begin{aligned} \text{GCF}(81, 576) &= 9 \ 81x^2 - 576 &= 9(9x^2 - 64) \end{aligned} $$ ## Apply the difference of squares formula $$ \begin{aligned} 9x^2 - 64 &= (3x)^2 - 8^2 \ &= (3x - 8)(3x + 8) \end{aligned} $$ ## Combine factors into fully factored form $$ 81x^2 - 576 = 9(3x - 8)(3x + 8) $$

(A) $(9x - 24)(9x + 24)$

(B) $9(3x + 8)(3x - 8)$

(C) None of these

(D) $3(3x - 8)^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Factoring" ] }

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Apply the difference of squares formula

Combine factors into fully factored form

Answer: