what is the product?
$(4y - 3)(2y^2 + 3y - 5)$

* $8y^3 + 3y + 15$
* $8y^3 - 23y + 15$
* $8y^3 - 6y^2 - 17y + 15$
* $8y^3 + 6y^2 - 29y + 15$

Question

what is the product?
$(4y - 3)(2y^2 + 3y - 5)$

* $8y^3 + 3y + 15$
* $8y^3 - 23y + 15$
* $8y^3 - 6y^2 - 17y + 15$
* $8y^3 + 6y^2 - 29y + 15$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication", "Polynomial Operations" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Polynomial Operations", "Like Terms" ] } ## Distribute the terms of the binomial $$ (4y - 3)(2y^2 + 3y - 5) = 4y(2y^2 + 3y - 5) - 3(2y^2 + 3y - 5) $$ ## Expand each distributed part $$ \begin{aligned} 4y(2y^2 + 3y - 5) &= 8y^3 + 12y^2 - 20y \ -3(2y^2 + 3y - 5) &= -6y^2 - 9y + 15 \end{aligned} $$ ## Combine like terms $$ \begin{aligned} (8y^3 + 12y^2 - 20y) + (-6y^2 - 9y + 15) &= 8y^3 + (12y^2 - 6y^2) + (-20y - 9y) + 15 \ &= 8y^3 + 6y^2 - 29y + 15 \end{aligned} $$

(A) $8y^3 + 3y + 15$

(B) $8y^3 - 23y + 15$

(C) $8y^3 - 6y^2 - 17y + 15$

(D) $8y^3 + 6y^2 - 29y + 15$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Distribute the terms of the binomial

Expand each distributed part

Combine like terms

Answer: