multiply the polynomial by the monomial using the distributive property and/or the product rule of exponents.

$(-x)(-4x^2 - 8)$

Question

multiply the polynomial by the monomial using the distributive property and/or the product rule of exponents.

$(-x)(-4x^2 - 8)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Multiplying Monomial by Polynomial", "Product Rule of Exponents" ], "new_concepts": [], "current_concepts": [ "Multiplying Monomial by Polynomial", "Product Rule of Exponents", "Distributive Property with Polynomials" ] } ## Apply the distributive property Using the *Multiplying Monomial by Polynomial* knowledge point $$ (-x)(-4x^2 - 8) = (-x)(-4x^2) + (-x)(-8) $$ ## Multiply the terms Using the *Product Rule of Exponents* knowledge point $$ \begin{aligned} (-x)(-4x^2) &= 4x^{1+2} = 4x^3\ (-x)(-8) &= 8x\ (-x)(-4x^2 - 8) &= 4x^3 + 8x \end{aligned} $$ Multiply the polynomial by the monomial using the distributive property and/or the product rule of exponents. $$(-x)(-4x^2 - 8) =$$ $4x^3 + 8x$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Monomial by Polynomial" ] }

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Question

Explanation:

Apply the distributive property

Multiply the terms

Answer: