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📅 April 30, 2026 👤 scraface

Apr 30, 2026

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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 \\
3(x^2 - 2x + 3) = 3x^2 - 6x + 9
Now combine all terms:
x^4 - 2x^3 + 3x^2 + 2x^3 - 4x^2 + 6x + 3x^2 - 6x + 9

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