multiplying multivariable polynomials

find the product of $(-d + e)(4e + d)$. which statements are true? check all that apply.

there are 2 terms in the product.
there are 3 terms in the product.
there are 4 terms in the product.
the product is degree 1.
the product is degree 2.
the product is degree 4.

Question

multiplying multivariable polynomials

find the product of $(-d + e)(4e + d)$. which statements are true? check all that apply.

there are 2 terms in the product.
  there are 3 terms in the product.
  there are 4 terms in the product.
  the product is degree 1.
  the product is degree 2.
  the product is degree 4.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Degree", "Polynomial Multiplication", "Like Terms" ], "new_concepts": [], "current_concepts": [ "Polynomial Degree", "Polynomial Multiplication", "Like Terms" ] } ## Expand the polynomial product $$ \begin{aligned} (-d + e)(4e + d) &= -d(4e + d) + e(4e + d) \ &= -4de - d^2 + 4e^2 + ed \end{aligned} $$ ## Combine like terms $$ \begin{aligned} -4de + ed &= -3de \ \text{Product} &= -d^2 - 3de + 4e^2 \end{aligned} $$ ## Analyze terms and degree $$ \begin{aligned} &\text{Terms: } -d^2, -3de, 4e^2 \implies 3 \text{ terms} \ &\text{Degree of } -d^2 \implies 2 \ &\text{Degree of } -3de \implies 1 + 1 = 2 \ &\text{Degree of } 4e^2 \implies 2 \ &\text{Product Degree} \implies 2 \end{aligned} $$

There are 2 terms in the product.

There are 3 terms in the product.

There are 4 terms in the product.

The product is degree 1.

The product is degree 2.

The product is degree 4.

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Expand the polynomial product

Combine like terms

Analyze terms and degree

Answer: