what is the product of $(p^3)(2p^2 - 4p)(3p^2 - 1)$?

$6p^7 + 4p^4$

$6p^7 - 2p^5 - 12p^5 + 4p^3$

$6p^7 - 12p^6 - 2p^5 + 4p^4$

$6p^{12} - 14p^6 + 4p^3$

Question

what is the product of $(p^3)(2p^2 - 4p)(3p^2 - 1)$?

$6p^7 + 4p^4$

$6p^7 - 2p^5 - 12p^5 + 4p^3$

$6p^7 - 12p^6 - 2p^5 + 4p^4$

$6p^{12} - 14p^6 + 4p^3$

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": [ "Multiplying Polynomials", "Product of Powers" ], "current_concepts": [ "Multiplying Polynomials", "Product of Powers" ] } ## Multiply the binomials first $$ \begin{aligned} (2p^2 - 4p)(3p^2 - 1) &= (2p^2)(3p^2) + (2p^2)(-1) + (-4p)(3p^2) + (-4p)(-1) \ &= 6p^4 - 2p^2 - 12p^3 + 4p \end{aligned} $$ ## Multiply the result by the monomial $$ \begin{aligned} (p^3)(6p^4 - 12p^3 - 2p^2 + 4p) &= (p^3)(6p^4) - (p^3)(12p^3) - (p^3)(2p^2) + (p^3)(4p) \ &= 6p^7 - 12p^6 - 2p^5 + 4p^4 \end{aligned} $$

(A) $6p^7 + 4p^4$

(B) $6p^7 - 2p^5 - 12p^5 + 4p^3$

(C) $6p^7 - 12p^6 - 2p^5 + 4p^4$

(D) $6p^{12} - 14p^6 + 4p^3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Multiply the binomials first

Multiply the result by the monomial

Answer: