\(3a + 2)(a - 6) + (a - 5)(a - 5)\

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "FOIL Method", "Square of a Binomial Difference", "Polynomial Addition", "Polynomial Simplification" ], "new_concepts": [], "current_concepts": [ "FOIL Method", "Square of a Binomial Difference", "Polynomial Addition", "Polynomial Simplification" ] } ## Expand the first product Using the *FOIL Method* knowledge point $$ \begin{aligned} (3a + 2)(a - 6) &= (3a)(a) + (3a)(-6) + (2)(a) + (2)(-6) \ &= 3a^2 - 18a + 2a - 12 \ &= 3a^2 - 16a - 12 \end{aligned} $$ ## Expand the second product Using the *Square of a Binomial Difference* knowledge point $$ \begin{aligned} (a - 5)(a - 5) &= (a - 5)^2 \ &= a^2 - 2(a)(5) + 5^2 \ &= a^2 - 10a + 25 \end{aligned} $$ ## Combine the expanded expressions Using the *Polynomial Addition* knowledge point $$ \begin{aligned} (3a^2 - 16a - 12) + (a^2 - 10a + 25) \end{aligned} $$ ## Group and combine like terms Using the *Polynomial Simplification* knowledge point $$ \begin{aligned} &= (3a^2 + a^2) + (-16a - 10a) + (-12 + 25) \ &= 4a^2 - 26a + 13 \end{aligned} $$ $4a^2 - 26a + 13$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Simplification" ] }

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Question

Explanation:

Expand the first product

Expand the second product

Combine the expanded expressions

Group and combine like terms

Answer: