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Home » Case 2:** \( racr+1r-1 = rac{3 - \sqrt5}2 \) - Sterling Industries

Case 2:** \( racr+1r-1 = rac{3 - \sqrt5}2 \) - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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Question: Factor the expression $ x^4 - 16y^4 + 8x^2 + 64 $.
Solution: Group the expression:
x^4 - 16y^4 + 8x^2 + 64 = (x^4 + 8x^2 + 16) - (16y^4 - 64)
Note that $ x^4 + 8x^2 + 16 = (x^2 + 4)^2 $ and $ 16y^4 - 64 = 16(y^4...
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 th...
So the full expression becomes:
Now factor the remaining terms:
Letâs try factoring by grouping. Try factoring $ x^4 + 8x^2 + 16 $ a...

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