multiply.

\(\sqrt{6} - 8\sqrt{10})(2\sqrt{10} + 5\sqrt{6})\

simplify your answer as much as possible.

Question

multiply.

\(\sqrt{6} - 8\sqrt{10})(2\sqrt{10} + 5\sqrt{6})\

simplify your answer as much as possible.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Multiplication", "Simplifying Radicals" ], "new_concepts": [], "current_concepts": [ "Radical Multiplication", "Simplifying Radicals", "Algebraic Expressions" ] } ## Expand the product of binomials $$ (\sqrt{6}-8\sqrt{10})(2\sqrt{10}+5\sqrt{6}) = \sqrt{6}(2\sqrt{10}) + \sqrt{6}(5\sqrt{6}) - 8\sqrt{10}(2\sqrt{10}) - 8\sqrt{10}(5\sqrt{6}) $$ ## Multiply individual terms $$ \begin{aligned} \sqrt{6}(2\sqrt{10}) &= 2\sqrt{60} \ \sqrt{6}(5\sqrt{6}) &= 5 \times 6 = 30 \ -8\sqrt{10}(2\sqrt{10}) &= -16 \times 10 = -160 \ -8\sqrt{10}(5\sqrt{6}) &= -40\sqrt{60} \end{aligned} $$ ## Combine and simplify terms $$ \begin{aligned} 30 - 160 + 2\sqrt{60} - 40\sqrt{60} &= -130 - 38\sqrt{60} \ &= -130 - 38\sqrt{4 \times 15} \ &= -130 - 38(2\sqrt{15}) \ &= -130 - 76\sqrt{15} \end{aligned} $$ Multiply. $$ (\sqrt{6}-8\sqrt{10})(2\sqrt{10}+5\sqrt{6}) $$ Simplify your answer as much as possible. $-130-76\sqrt{15}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Radicals" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the product of binomials

Multiply individual terms

Combine and simplify terms

Answer: