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g) \( y^{9}-125 \)

Ask by Boone Pope. in South Africa
Feb 09,2025

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\( y^{9} - 125 = (y^{3} - 5)(y^{6} + 5y^{3} + 25) \)

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The expression \( y^9 - 125 \) can be recognized as a difference of powers, specifically \( y^9 - 5^3 \). This can be factored using the difference of cubes formula, which states that \( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \). Applying this to our expression, we can rewrite it in a factorable form. Additionally, the expression can also be interestingly approached through its real-world applications. For instance, polynomials like \( y^9 - 125 \) appear frequently in physics when calculating trajectories, wave functions, or energy levels in quantum mechanics. The factoring process can simplify complex calculations, making it easier for scientists and engineers to analyze real-world problems!

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