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Home » Taking the square root of both sides, we find: - 500apps

Taking the square root of both sides, we find: - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Recognize the expression as a difference of squares:

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

📌 Now, note that \(x^2 - 4y^2\) is also a difference of squares:

📌 x^2 - 4y^2 = (x - 2y)(x + 2y)

📌 The term \(x^2 + 4y^2\) cannot be factored over the reals.

📌 Thus, the complete factorization is:

📌 Final answer: \(\boxed{(x - 2y)(x + 2y)(x^2 + 4y^2)}\)

📌 A sequence of five real numbers forms an arithmetic progression, and the sum of the squares of the terms is 1100. If the common difference is 3 and the middle term is 2, what is the first term?

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