Simplify (2x – 5y)³ – (2x + 5y)³

Simplify : \((2x – 5y)^3 – (2x + 5y)^3\)

\[ (2x – 5y)^3 – (2x + 5y)^3 \] \[ = \left[(2x – 5y) – (2x + 5y)\right] \left[(2x – 5y)^2 + (2x – 5y)(2x + 5y) + (2x + 5y)^2\right] \] \[ = (-10y) \left[(4x^2 – 20xy + 25y^2) + (4x^2 – 25y^2) + (4x^2 + 20xy + 25y^2)\right] \] \[ = (-10y)(12x^2 + 25y^2) \] \[ = -120x^2y – 250y^3 \]

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