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scouts guide to the zombie apocalypse - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \frac{5}{\sqrt{7} + \sqrt{2}} \cdot \frac{\sqrt{7} - \sqrt{2}}{\sqrt{7} - \sqrt{2}} = \frac{5(\sqrt{7} - \sqrt{2})}{(\sqrt{7} + \sqrt{2})(\sqrt{7} - \sqrt{2})}

📌 Simplify the denominator using the difference of squares:

📌 \frac{5(\sqrt{7} - \sqrt{2})}{5} = \sqrt{7} - \sqrt{2}

📌 Final answer: $ \boxed{\sqrt{7} - \sqrt{2}} $

📌 Question: Expand the product $ (x^2 + 2x + 3)(x^2 - 2x + 3) $.

📌 Use distributive property (FOIL-like expansion):

📌 x^2(x^2 - 2x + 3) = x^4 - 2x^3 + 3x^2 \\

📌 2x(x^2 - 2x + 3) = 2x^3 - 4x^2 + 6x \\

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