28) \( 16 x y-3 x-6 x^{2}+8 y \)
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The Deep Dive
To factor the expression \( 16xy - 3x - 6x^{2} + 8y \), you can rearrange it into a more manageable form: \( -6x^{2} + 16xy + 8y - 3x \). Grouping the terms will help. Combining like terms gives you \(-6x^{2} + (-3x + 16xy + 8y)\). Now, factor out common factors in groups, which can lead to discovering potential binomials. Keep in mind that factorization often involves trial and error, so don't hesitate to play around with different combinations! For a little historical twist, did you know that factoring polynomials has been around since ancient civilizations? The Babylonians and Greeks made significant contributions to algebra and geometric methods, paving the way for modern polynomial algebra. It's fascinating how these ancient techniques still influence current mathematical practices!