1. simplify $(-10a^3b)(2a^2b)$.

$-8a^5b^2$

$-8a^6b$

$-20a^6b^2$

$-20a^5b^2$

Question

1. simplify $(-10a^3b)(2a^2b)$.

$-8a^5b^2$

$-8a^6b$

$-20a^6b^2$

$-20a^5b^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Algebraic Simplification" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Algebraic Simplification", "Monomial Multiplication" ] } ## Group coefficients and variables $$ (-10 \cdot 2) \cdot (a^3 \cdot a^2) \cdot (b \cdot b) $$ ## Multiply coefficients $$ -10 \cdot 2 = -20 $$ ## Apply exponent rules to variables $$ \begin{aligned} a^3 \cdot a^2 &= a^{3+2} = a^5 \ b^1 \cdot b^1 &= b^{1+1} = b^2 \ (-10a^3b)(2a^2b) &= -20a^5b^2 \end{aligned} $$

(A) $-8a^5b^2$

(B) $-8a^6b$

(C) $-20a^6b^2$

(D) $-20a^5b^2$

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

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QUESTION IMAGE

Question

Explanation:

Group coefficients and variables

Multiply coefficients

Apply exponent rules to variables

Answer: