adding which terms to $3x^2y$ would result in a monomial? check all that apply.

$3xy$
$-12x^2y$
$2x^2y^2$
$7xy^2$
$-10x^2$
$4x^2y$
$3x^3$

Question

adding which terms to $3x^2y$ would result in a monomial? check all that apply.

$3xy$
  $-12x^2y$
  $2x^2y^2$
  $7xy^2$
  $-10x^2$
  $4x^2y$
  $3x^3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Terms", "Polynomial Addition" ], "new_concepts": [ "Like Terms", "Monomial Definition" ], "current_concepts": [ "Polynomial Terms", "Polynomial Addition", "Like Terms", "Monomial Definition" ] } ## Identify the condition for a sum to be a monomial $$ 3x^2y + \text{term} = \text{monomial} \iff \text{term is a like term to } 3x^2y $$ ## Determine the variable part of like terms $$ \text{Variable part} = x^2y $$ ## Evaluate the given options $$ \begin{aligned} &3xy \implies \text{Unlike term} \ &-12x^2y \implies \text{Like term} \ &2x^2y^2 \implies \text{Unlike term} \ &7xy^2 \implies \text{Unlike term} \ &-10x^2 \implies \text{Unlike term} \ &4x^2y \implies \text{Like term} \ &3x^3 \implies \text{Unlike term} \end{aligned} $$

3xy

-12x^2y

2x^2y^2

7xy^2

-10x^2

4x^2y

3x^3

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

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QUESTION IMAGE

Question

Explanation:

Identify the condition for a sum to be a monomial

Determine the variable part of like terms

Evaluate the given options

Answer: