question 1

evaluate $x^3 + y^2 + 2xy - 5$ when $x = 3$ and $y = 5$.

159
84
77
20

question 2

evaluate $2x^2 - 5y^2 + 2xy + x - 2$ when $x = 2$ and $y = 1$.

3
-5
7
-26

question 3

add the following multivariable polynomials:
$(3x^2 + 2xy + 4y^2) + (x^2 - 5xy - 2y^2)$

$2x^2y^2 - 3xy$
$4x^2 - 3xy + 6y^2$
$3x^4 - 3x^2 + 2y^4$
$4x^2 - 3xy + 2y^2$

Question

question 1

evaluate $x^3 + y^2 + 2xy - 5$ when $x = 3$ and $y = 5$.

159
84
77
20

question 2

evaluate $2x^2 - 5y^2 + 2xy + x - 2$ when $x = 2$ and $y = 1$.

3
-5
7
-26

question 3

add the following multivariable polynomials:
$(3x^2 + 2xy + 4y^2) + (x^2 - 5xy - 2y^2)$

$2x^2y^2 - 3xy$
$4x^2 - 3xy + 6y^2$
$3x^4 - 3x^2 + 2y^4$
$4x^2 - 3xy + 2y^2$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Evaluation", "Polynomial Addition" ], "new_concepts": [], "current_concepts": [ "Polynomial Evaluation", "Polynomial Addition", "Combining Like Terms" ] } ## Evaluate Question 1 $$ \begin{aligned} &\text{Expression: } x^3 + y^2 + 2xy - 5 \quad (x = 3, y = 5)\ &\text{Substitution: } 3^3 + 5^2 + 2(3)(5) - 5\ &\text{Calculation: } 27 + 25 + 30 - 5 = 77 \end{aligned} $$ ## Evaluate Question 2 $$ \begin{aligned} &\text{Expression: } 2x^2 - 5y^2 + 2xy + x - 2 \quad (x = 2, y = 1)\ &\text{Substitution: } 2(2)^2 - 5(1)^2 + 2(2)(1) + 2 - 2\ &\text{Calculation: } 2(4) - 5(1) + 4 + 2 - 2 = 8 - 5 + 4 = 7 \end{aligned} $$ ## Evaluate Question 3 $$ \begin{aligned} &\text{Expression: } (3x^2 + 2xy + 4y^2) + (x^2 - 5xy - 2y^2)\ &\text{Group like terms: } (3x^2 + x^2) + (2xy - 5xy) + (4y^2 - 2y^2)\ &\text{Simplify: } 4x^2 - 3xy + 2y^2 \end{aligned} $$ ## Question 1 (A) 159

(B) 84

(C) 77

(D) 20 ## Question 2 (A) 3

(B) -5

(C) 7

(D) -26 ## Question 3 (A) $2x^2y^2 - 3xy$

(B) $4x^2 - 3xy + 6y^2$

(C) $3x^4 - 3x^2 + 2y^4$

(D) $4x^2 - 3xy + 2y^2$

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

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