find the product of $(4z^2 + 7z - 8)$ and $(-z + 3)$.
the product of $(4z^2 + 7z - 8)$ and $(-z + 3)$ is $-4z^3 + \quadz^2 + \quadz - 24$.

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication", "Like Terms" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Like Terms", "Polynomial Operations" ] } ## Set up the multiplication expression $$ (4z^2 + 7z - 8)(-z + 3) $$ ## Distribute each term $$ \begin{aligned} (4z^2 + 7z - 8)(-z + 3) &= 4z^2(-z + 3) + 7z(-z + 3) - 8(-z + 3) \ &= -4z^3 + 12z^2 - 7z^2 + 21z + 8z - 24 \end{aligned} $$ ## Combine like terms $$ \begin{aligned} -4z^3 + (12 - 7)z^2 + (21 + 8)z - 24 = -4z^3 + 5z^2 + 29z - 24 \end{aligned} $$ Find the product of $(4z^2 + 7z - 8)$ and $(-z + 3)$. The product of $(4z^2 + 7z - 8)$ and $(-z + 3)$ is $-4z^3 +$ 5$z^2 +$ 29$z - 24$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplication" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the multiplication expression

Distribute each term

Combine like terms

Answer: