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