$3c^2 + 2d)(-5c^2 + d)\
select all of the partial products for the multiplication problem above.
- \(2d^2$
- $3cd^3$
- $-15c^4$
- $-10c^2 d$
- $-15c^2$
- $3c^2 d$

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Distributive Property", "Multiplying Polynomials" ], "new_concepts": [ "Partial Products" ], "current_concepts": [ "Distributive Property", "Multiplying Polynomials", "Partial Products" ] } ## Apply the distributive property Using the *Distributive Property* and *Multiplying Polynomials* knowledge points $$ (3c^2 + 2d)(-5c^2 + d) = 3c^2(-5c^2 + d) + 2d(-5c^2 + d) $$ ## Calculate individual partial products Using the *Multiplying Polynomials* knowledge point $$ \begin{aligned} &\text{First term: } 3c^2 \cdot (-5c^2) = -15c^4\ &\text{Second term: } 3c^2 \cdot d = 3c^2d\ &\text{Third term: } 2d \cdot (-5c^2) = -10c^2d\ &\text{Fourth term: } 2d \cdot d = 2d^2 \end{aligned} $$ ## Match with the given options Using the *Multiplying Polynomials* knowledge point $$ \begin{aligned} &2d^2 \quad (\text{Matched})\ &3cd^3 \quad (\text{Not matched})\ &-15c^4 \quad (\text{Matched})\ &-10c^2d \quad (\text{Matched})\ &-15c^2 \quad (\text{Not matched})\ &3c^2d \quad (\text{Matched}) \end{aligned} $$

$2d^2$

$3cd^3$

$-15c^4$

$-10c^2d$

$-15c^2$

$3c^2d$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the distributive property

Calculate individual partial products

Match with the given options

Answer: