multiplying multivariable polynomials

what is the product of $2x + y$ and $5x - y + 3$?

$\quadx^2 + \quadxy + \quadx - \quady^2 + \quady$

Question

multiplying multivariable polynomials

what is the product of $2x + y$ and $5x - y + 3$?

$\quadx^2 + \quadxy + \quadx - \quady^2 + \quady$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Multivariable Polynomial Multiplication" ], "current_concepts": [ "Polynomial Multiplication", "Multivariable Polynomials", "Multivariable Polynomial Multiplication" ] } ## Set up the multiplication expression $$ (2x + y)(5x - y + 3) $$ ## Expand using the distributive property $$ \begin{aligned} (2x + y)(5x - y + 3) &= 2x(5x - y + 3) + y(5x - y + 3) \ &= (10x^2 - 2xy + 6x) + (5xy - y^2 + 3y) \end{aligned} $$ ## Combine like terms and arrange in the target format $$ \begin{aligned} &= 10x^2 + (-2xy + 5xy) + 6x - y^2 + 3y \ &= 10x^2 + 3xy + 6x - 1y^2 + 3y \end{aligned} $$ What is the product of $2x + y$ and $5x - y + 3$? 10$x^2 +$ 3$xy +$ 6$x -$ 1$y^2 +$ 3$y$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Multivariable Polynomial Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the multiplication expression

Expand using the distributive property

Combine like terms and arrange in the target format

Answer: