\frac{b^3 - 21}{5b + 9} \text{ when } b = 3

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Substitution", "Order of Operations", "Fraction Arithmetic" ], "new_concepts": [], "current_concepts": [ "Algebraic Substitution", "Order of Operations", "Fraction Arithmetic" ] } ## Substitute the value of b into the expression $$ \frac{3^3 - 21}{5(3) + 9} $$ ## Simplify the numerator and denominator $$ \begin{aligned} \text{Numerator: } & 3^3 - 21 = 27 - 21 = 6 \ \text{Denominator: } & 5(3) + 9 = 15 + 9 = 24 \end{aligned} $$ ## Reduce the fraction to simplest form $$ \frac{6}{24} = \frac{1}{4} $$ $\frac{1}{4}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Substitution" ] }

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Question

Explanation:

Substitute the value of b into the expression

Simplify the numerator and denominator

Reduce the fraction to simplest form

Answer: