5. expand the following: $9x(3x^2 + 2x - 9)$

$27x^2 + 18x - 81$
$27x^3 + 18x^2 - 81x$
$12x^3 + 11x^2 - x$
$27x^3 + 18x^2 - 18x$

Question

5. expand the following: $9x(3x^2 + 2x - 9)$

$27x^2 + 18x - 81$
$27x^3 + 18x^2 - 81x$
$12x^3 + 11x^2 - x$
$27x^3 + 18x^2 - 18x$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Polynomial Expansion", "Distributive Property" ], "current_concepts": [ "Polynomial Expansion", "Distributive Property" ] } ## Distribute the outer term to each term inside the parentheses $$ 9x \cdot (3x^2 + 2x - 9) = (9x \cdot 3x^2) + (9x \cdot 2x) - (9x \cdot 9) $$ ## Simplify each multiplied term using exponent rules $$ \begin{aligned} 9x \cdot 3x^2 &= 27x^3 \ 9x \cdot 2x &= 18x^2 \ 9x \cdot 9 &= 81x \end{aligned} $$ ## Combine the simplified terms into the final polynomial $$ 27x^3 + 18x^2 - 81x $$

(A) $27x^2 + 18x - 81$

(B) $27x^3 + 18x^2 - 81x$

(C) $12x^3 + 11x^2 - x$

(D) $27x^3 + 18x^2 - 18x$

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

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QUESTION IMAGE

Question

Explanation:

Distribute the outer term to each term inside the parentheses

Simplify each multiplied term using exponent rules

Combine the simplified terms into the final polynomial

Answer: