what is the product?

$(-2d^2 + s)(5d^2 - 6s)$

- $-10d^4 + 17d^4s^2 - 6s^2$
- $-10d^4 - 7d^2s - 6s^2$
- $-10d^4 + 17d^2s + 6s^2$
- $-10d^4 + 17d^2s - 6s^2$

Question

what is the product?

$(-2d^2 + s)(5d^2 - 6s)$

- $-10d^4 + 17d^4s^2 - 6s^2$
- $-10d^4 - 7d^2s - 6s^2$
- $-10d^4 + 17d^2s + 6s^2$
- $-10d^4 + 17d^2s - 6s^2$

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", "Distributive Property" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Distributive Property" ] } ## Apply the distributive property $$ (-2d^2 + s)(5d^2 - 6s) = (-2d^2)(5d^2) + (-2d^2)(-6s) + (s)(5d^2) + (s)(-6s) $$ ## Multiply individual terms $$ \begin{aligned} (-2d^2)(5d^2) &= -10d^4 \ (-2d^2)(-6s) &= 12d^2s \ (s)(5d^2) &= 5d^2s \ (s)(-6s) &= -6s^2 \end{aligned} $$ ## Combine like terms $$ \begin{aligned} -10d^4 + 12d^2s + 5d^2s - 6s^2 &= -10d^4 + (12 + 5)d^2s - 6s^2 \ &= -10d^4 + 17d^2s - 6s^2 \end{aligned} $$

(A) $-10d^4 + 17d^4s^2 - 6s^2$

(B) $-10d^4 - 7d^2s - 6s^2$

(C) $-10d^4 + 17d^2s + 6s^2$

(D) $-10d^4 + 17d^2s - 6s^2$

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

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QUESTION IMAGE

Question

Explanation:

Apply the distributive property

Multiply individual terms

Combine like terms

Answer: