use the chart to multiply the binomial by the trinomial.

$2y + 3)(3y^2 + 4y + 5)\

which polynomial is the correct product?

* \(15y^3 + 17y^2 + 22y + 15$
* $6y^3 + 17y^2 + 22y + 15$
* $6y^3 + 20y^2 + 22y + 15$
* $6y^3 + 17y^2 + 22y + 25$

Question

use the chart to multiply the binomial by the trinomial.

$2y + 3)(3y^2 + 4y + 5)\

which polynomial is the correct product?

* \(15y^3 + 17y^2 + 22y + 15$
* $6y^3 + 17y^2 + 22y + 15$
* $6y^3 + 20y^2 + 22y + 15$
* $6y^3 + 17y^2 + 22y + 25$

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", "Algebraic Simplification" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Algebraic Simplification" ] } ## Expand the expression using the distributive property $$ (2y + 3)(3y^2 + 4y + 5) = 2y(3y^2 + 4y + 5) + 3(3y^2 + 4y + 5) $$ ## Distribute terms $$ \begin{aligned} 2y(3y^2 + 4y + 5) &= 6y^3 + 8y^2 + 10y \ 3(3y^2 + 4y + 5) &= 9y^2 + 12y + 15 \end{aligned} $$ ## Combine like terms $$ \begin{aligned} (6y^3 + 8y^2 + 10y) + (9y^2 + 12y + 15) &= 6y^3 + (8y^2 + 9y^2) + (10y + 12y) + 15 \ &= 6y^3 + 17y^2 + 22y + 15 \end{aligned} $$

(A) $15y^3 + 17y^2 + 22y + 15$

(B) $6y^3 + 17y^2 + 22y + 15$

(C) $6y^3 + 20y^2 + 22y + 15$

(D) $6y^3 + 17y^2 + 22y + 25$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Expand the expression using the distributive property

Distribute terms

Combine like terms

Answer: