\2x^3(x^3 + 3x^2 - 2x + 5)\

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distributive Property with Monomials", "Exponent Rules" ], "new_concepts": [], "current_concepts": [ "Distributive Property with Monomials", "Exponent Rules", "Polynomial Expansion" ] } ## Apply the distributive property $$ 2x^3(x^3 + 3x^2 - 2x + 5) = (2x^3 \cdot x^3) + (2x^3 \cdot 3x^2) - (2x^3 \cdot 2x) + (2x^3 \cdot 5) $$ ## Simplify each term using exponent rules $$ \begin{aligned} 2x^3 \cdot x^3 &= 2x^{3+3} = 2x^6 \ 2x^3 \cdot 3x^2 &= 6x^{3+2} = 6x^5 \ -2x^3 \cdot 2x &= -4x^{3+1} = -4x^4 \ 2x^3 \cdot 5 &= 10x^3 \end{aligned} $$ ## Combine the simplified terms $$ 2x^6 + 6x^5 - 4x^4 + 10x^3 $$ $2x^6 + 6x^5 - 4x^4 + 10x^3$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Distributive Property with Monomials" ] }

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Explanation:

Apply the distributive property

Simplify each term using exponent rules

Combine the simplified terms

Answer: