multiply the binomials using the foil method. combine like terms.

\(-2x - 2)(3x - 8)\

Question

multiply the binomials using the foil method. combine like terms.

\(-2x - 2)(3x - 8)\

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", "Polynomial Simplification" ], "new_concepts": [], "current_concepts": [ "FOIL Method", "Polynomial Multiplication", "Polynomial Simplification" ] } ## Identify the expression and method We are given the product of two binomials to expand: $$ (-2x - 2)(3x - 8) $$ We will apply the FOIL method to multiply them. ## Apply the FOIL method Using the *FOIL Method* knowledge point $$ \begin{aligned} \text{First (F):} \quad & (-2x)(3x) = -6x^2 \ \text{Outer (O):} \quad & (-2x)(-8) = 16x \ \text{Inner (I):} \quad & (-2)(-3x) \implies (-2)(3x) = -6x \ \text{Last (L):} \quad & (-2)(-8) = 16 \end{aligned} $$ ## Combine the terms Using the *Polynomial Simplification* knowledge point $$ \begin{aligned} \text{Sum:} \quad & -6x^2 + 16x - 6x + 16 \ \text{Simplified:} \quad & -6x^2 + 10x + 16 \end{aligned} $$ $-6x^2 + 10x + 16$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the expression and method

Apply the FOIL method

Combine the terms

Answer: