use the distributive property to remove the parentheses.

$(6z^2 - 8z^5 + 3)7z^4$

simplify your answer as much as possible.

Question

use the distributive property to remove the parentheses.

$(6z^2 - 8z^5 + 3)7z^4$

simplify your answer as much as possible.

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", "Monomial Multiplication" ] } ## Apply the distributive property $$ (6z^2 - 8z^5 + 3) \cdot 7z^4 = (6z^2 \cdot 7z^4) - (8z^5 \cdot 7z^4) + (3 \cdot 7z^4) $$ ## Multiply the terms using exponent rules $$ \begin{aligned} 6z^2 \cdot 7z^4 &= 42z^{2+4} = 42z^6 \ 8z^5 \cdot 7z^4 &= 56z^{5+4} = 56z^9 \ 3 \cdot 7z^4 &= 21z^4 \end{aligned} $$ ## Combine the simplified terms $$ 42z^6 - 56z^9 + 21z^4 $$ $42z^6 - 56z^9 + 21z^4$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Distributive Property with Monomials" ] }

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Question

Explanation:

Apply the distributive property

Multiply the terms using exponent rules

Combine the simplified terms

Answer: