use the chart to multiply the binomial by the trinomial.

$(y + 3)(y^2 - 3y + 9)$

what is the product?

$y^3 + 27$
$y^3 - 27$
$y^3 - 6y^2 + 27$
$y^3 + 6y^2 + 27$

Question

use the chart to multiply the binomial by the trinomial.

$(y + 3)(y^2 - 3y + 9)$

what is the product?

$y^3 + 27$
$y^3 - 27$
$y^3 - 6y^2 + 27$
$y^3 + 6y^2 + 27$

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": [ "Sum of Cubes" ], "current_concepts": [ "Polynomial Multiplication", "Algebraic Simplification", "Sum of Cubes" ] } ## Set up the polynomial multiplication $$ (y + 3)(y^2 - 3y + 9) $$ ## Expand using the distributive property $$ \begin{aligned} (y + 3)(y^2 - 3y + 9) &= y(y^2 - 3y + 9) + 3(y^2 - 3y + 9) \ &= (y^3 - 3y^2 + 9y) + (3y^2 - 9y + 27) \end{aligned} $$ ## Combine like terms $$ \begin{aligned} y^3 + (-3y^2 + 3y^2) + (9y - 9y) + 27 &= y^3 + 0y^2 + 0y + 27 \ &= y^3 + 27 \end{aligned} $$

(A) $y^3 + 27$

(B) $y^3 - 27$

(C) $y^3 - 6y^2 + 27$

(D) $y^3 + 6y^2 + 27$

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

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QUESTION IMAGE

Question

Explanation:

Set up the polynomial multiplication

Expand using the distributive property

Combine like terms

Answer: