what value of $c$ makes the statement true?
\-2x^3(cx^3 + x^2) = -10x^6 - 2x^5\
$c =$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distributive Property", "Product of Powers" ], "new_concepts": [], "current_concepts": [ "Distributive Property", "Product of Powers", "Simplifying Monomials" ] } ## Expand the left side of the equation $$ -2x^3(cx^3 + x^2) = (-2x^3)(cx^3) + (-2x^3)(x^2) $$ ## Simplify the terms using exponent rules $$ -2cx^6 - 2x^5 $$ ## Equate coefficients to solve for c $$ \begin{aligned} -2cx^6 - 2x^5 &= -10x^6 - 2x^5 \ -2c &= -10 \ c &= 5 \end{aligned} $$ What value of $c$ makes the statement true? $-2x^3(cx^3 + x^2) = -10x^6 - 2x^5$ $c =$ 5 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Monomials" ] }

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Question

Explanation:

Expand the left side of the equation

Simplify the terms using exponent rules

Equate coefficients to solve for c

Answer: