expand and simplify

$(1 - 3\sqrt{3})(2 - \sqrt{12})$

Question

expand and simplify

$(1 - 3\sqrt{3})(2 - \sqrt{12})$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distributive Property", "Simplifying Radicals", "Operations with Radicals" ], "new_concepts": [], "current_concepts": [ "Distributive Property", "Simplifying Radicals", "Operations with Radicals" ] } ## Simplify the radical term $$ \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} $$ ## Expand the expression using FOIL $$ \begin{aligned} (1 - 3\sqrt{3})(2 - 2\sqrt{3}) &= 1(2) - 1(2\sqrt{3}) - 3\sqrt{3}(2) + 3\sqrt{3}(2\sqrt{3}) \ &= 2 - 2\sqrt{3} - 6\sqrt{3} + 6(3) \ &= 2 - 8\sqrt{3} + 18 \end{aligned} $$ ## Combine like terms $$ 2 + 18 - 8\sqrt{3} = 20 - 8\sqrt{3} $$ $20 - 8\sqrt{3}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Operations with Radicals" ] }

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Question

Explanation:

Simplify the radical term

Expand the expression using FOIL

Combine like terms

Answer: