what is the product of the binomials $(4a - 1)$ and $(2b + 3)$?

$18ab - 3$
$8a^2b^2 + 10ab - 3$
$6ab + 7a - 2b - 3$
$8ab + 12a - 2b - 3$

Question

what is the product of the binomials $(4a - 1)$ and $(2b + 3)$?

$18ab - 3$
$8a^2b^2 + 10ab - 3$
$6ab + 7a - 2b - 3$
$8ab + 12a - 2b - 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication", "Distributive Property" ], "new_concepts": [ "Multivariable Polynomials" ], "current_concepts": [ "Polynomial Multiplication", "Distributive Property", "Multivariable Polynomials" ] } ## Set up the product of the binomials $$ (4a - 1)(2b + 3) $$ ## Apply the distributive property $$ (4a)(2b) + (4a)(3) + (-1)(2b) + (-1)(3) $$ ## Simplify each term $$ 8ab + 12a - 2b - 3 $$

(A) $18ab - 3$

(B) $8a^2b^2 + 10ab - 3$

(C) $6ab + 7a - 2b - 3$

(D) $8ab + 12a - 2b - 3$

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

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QUESTION IMAGE

Question

Explanation:

Set up the product of the binomials

Apply the distributive property

Simplify each term

Answer: