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Home » Why Beginners Fear Preterite – But It’s Easier Than You Think! - Midis

Why Beginners Fear Preterite – But It’s Easier Than You Think! - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Let $ a = x $, $ b = 2y - z $. Then:

📌 Now expand $ (2y - z)^2 $:

📌 x^2 - (4y^2 - 4yz + z^2) = x^2 - 4y^2 + 4yz - z^2

📌 Thus, the simplified expansion is $ oxed{x^2 - 4y^2 + 4yz - z^2} $.

📌 Question: Factor the expression $ 9x^2 - 30xy + 25y^2 - 16z^2 $ completely.

📌 First, group the first three terms:

📌 Note that $ 9x^2 - 30xy + 25y^2 = (3x - 5y)^2 $, a perfect square.

📌 This is a difference of squares: $ a^2 - b^2 = (a - b)(a + b) $, with $ a = 3x - 5y $, $ b = 4z $.

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