19) state whether each group contains like terms. justify your response.

a) $-a^3b, \frac{3}{5}a^3b, 4.2a^3b$

b) $25a^2, \frac{1}{2}a^2b, 8.99ab$

Question

19) state whether each group contains like terms. justify your response.

a) $-a^3b, \frac{3}{5}a^3b, 4.2a^3b$

b) $25a^2, \frac{1}{2}a^2b, 8.99ab$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Like Terms", "Algebraic Expressions" ], "current_concepts": [ "Like Terms", "Algebraic Expressions" ] } ## Analyze variable parts of group a $$ \begin{aligned} &\text{Term 1: } -a^3b \implies \text{Variable part: } a^3b\ &\text{Term 2: } \frac{3}{5}a^3b \implies \text{Variable part: } a^3b\ &\text{Term 3: } 4.2a^3b \implies \text{Variable part: } a^3b\ &\text{All variable parts are identical.} \end{aligned} $$ ## Analyze variable parts of group b $$ \begin{aligned} &\text{Term 1: } 25a^2 \implies \text{Variable part: } a^2\ &\text{Term 2: } \frac{1}{2}a^2b \implies \text{Variable part: } a^2b\ &\text{Term 3: } 8.99ab \implies \text{Variable part: } ab\ &\text{The variable parts are different.} \end{aligned} $$ ## Question 19a Yes, this group contains like terms because all three terms have the identical variable part $a^3b$. ## Question 19b No, this group does not contain like terms because the terms have different variable parts ($a^2$, $a^2b$, and $ab$). { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Like Terms" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze variable parts of group a

Analyze variable parts of group b

Answer:

Question 19a

Question 19b