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Question Number 183363 by Shrinava last updated on 25/Dec/22

$$\mathrm{Find}:$$$$2003\cdot {2005}^3-2004\cdot {2002}^3$$

Answered by Frix last updated on 25/Dec/22

$$(x-\frac{1}{2}){(x+\frac{3}{2})}^3-(x+\frac{1}{2}){(x-\frac{3}{2})}^3=8x^3$$$$\Rightarrow$$$$\mathrm{answer}\mathrm{is}8\times \frac{{4007}^3}{2^3}={4007}^3$$

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