which of the following is equivalent to $(p^3)(2p^2 - 4p)(3p^2 - 1)$?

$(p^3)(6p^4 - 12p^3 - 2p^2 + 4p)$
$(p^3)(6p^4 + 4p)$
$(2p^6 - 4p^3)(3p^2 - 1)$
$(2p^5 - 4p^4)(3p^5 - p^3)$

Question

which of the following is equivalent to $(p^3)(2p^2 - 4p)(3p^2 - 1)$?

$(p^3)(6p^4 - 12p^3 - 2p^2 + 4p)$
$(p^3)(6p^4 + 4p)$
$(2p^6 - 4p^3)(3p^2 - 1)$
$(2p^5 - 4p^4)(3p^5 - p^3)$

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", "FOIL Method" ], "current_concepts": [ "Multiplying Polynomials", "FOIL Method", "Product of Powers" ] } ## Identify the expression to simplify The given expression is: $$ (p^3)(2p^2 - 4p)(3p^2 - 1) $$ ## Multiply the binomials first Multiply the two binomial factors $(2p^2 - 4p)$ and $(3p^2 - 1)$ using the FOIL method: $$ \begin{aligned} (2p^2 - 4p)(3p^2 - 1) &= (2p^2)(3p^2) + (2p^2)(-1) + (-4p)(3p^2) + (-4p)(-1) \ &= 6p^4 - 2p^2 - 12p^3 + 4p \ &= 6p^4 - 12p^3 - 2p^2 + 4p \end{aligned} $$ ## Substitute back into the original expression Substitute the simplified product of the binomials back into the expression: $$ (p^3)(6p^4 - 12p^3 - 2p^2 + 4p) $$ This matches the first option.

(A) $(p^3)(6p^4 - 12p^3 - 2p^2 + 4p)$

(B) $(p^3)(6p^4 + 4p)$

(C) $(2p^6 - 4p^3)(3p^2 - 1)$

(D) $(2p^5 - 4p^4)(3p^5 - p^3)$

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

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QUESTION IMAGE

Question

Explanation:

Identify the expression to simplify

Multiply the binomials first

Substitute back into the original expression

Answer: