multiply.

$(2\sqrt{6} - 5)(4\sqrt{10} - 1)$

simplify your answer as much as possible.

Question

multiply.

$(2\sqrt{6} - 5)(4\sqrt{10} - 1)$

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": [ "Algebraic Expressions" ], "new_concepts": [ "Radical Multiplication", "Simplifying Radicals" ], "current_concepts": [ "Algebraic Expressions", "Radical Multiplication", "Simplifying Radicals" ] } ## Expand the expression using the FOIL method $$ (2\sqrt{6} - 5)(4\sqrt{10} - 1) = (2\sqrt{6})(4\sqrt{10}) - (2\sqrt{6})(1) - (5)(4\sqrt{10}) + (5)(1) $$ ## Multiply the individual terms $$ \begin{aligned} (2\sqrt{6})(4\sqrt{10}) &= 8\sqrt{60} \ -(2\sqrt{6})(1) &= -2\sqrt{6} \ -(5)(4\sqrt{10}) &= -20\sqrt{10} \ (5)(1) &= 5 \end{aligned} $$ ## Simplify the radical terms and combine $$ \begin{aligned} 8\sqrt{60} &= 8\sqrt{4 \times 15} = 8 \times 2\sqrt{15} = 16\sqrt{15} \ (2\sqrt{6} - 5)(4\sqrt{10} - 1) &= 16\sqrt{15} - 2\sqrt{6} - 20\sqrt{10} + 5 \end{aligned} $$ Multiply. $$ (2\sqrt{6}-5)(4\sqrt{10}-1) $$ Simplify your answer as much as possible. $16\sqrt{15}-2\sqrt{6}-20\sqrt{10}+5$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Radicals" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the expression using the FOIL method

Multiply the individual terms

Simplify the radical terms and combine

Answer: