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winged horse of greek myth - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Let $ A = x^2 + 4 $, $ B = y^2 + 2 $, and $ C = y^2 - 2 $, then:

📌 A^2 - 16BC = (A - 4\sqrt{BC})(A + 4\sqrt{BC})

📌 But this factoring is not ideal over real numbers. Instead, observe that $ x^4 - 16y^4 = (x^2)^2 - (4y^2)^2 = (x^2 - 4y^2)(x^2 + 4y^2) $.

📌 So the full expression becomes:

📌 Now factor the remaining terms:

📌 Letâs try factoring by grouping. Try factoring $ x^4 + 8x^2 + 16 $ and $ -16y^4 + 64 $ separately:

📌 x^4 + 8x^2 + 16 = (x^2 + 4)^2

📌 -16y^4 + 64 = -16(y^4 - 4) = -16(y^2 - 2)(y^2 + 2)

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